Polarization (waves)

Polarization (alsopolarisation) is a property applying to transversewaves that specifies the geometrical orientation of the oscillations.[1][2][3][4][5] In a transverse wave, the direction of the oscillation is transverse to the direction of motion of the wave, so the oscillations can have different directions perpendicular to the wave direction.[4] A simple example of a polarized transverse wave is vibrations traveling along a taut string (see image); for example, in a musical instrument like a guitar string. Depending on how the string is plucked, the vibrations can be in a vertical direction, horizontal direction, or at any angle perpendicular to the string; in contrast, in longitudinal waves, such as sound waves in a liquid or gas, the displacement of the particles in the oscillation is always in the direction of propagation, so these waves do not exhibit polarization. Transverse waves that exhibit polarization include electromagnetic waves such as light and radio waves, gravitational waves,[6] and transverse sound waves (shear waves) in solids. In some types of transverse waves, the wave displacement is limited to a single direction, so these also do not exhibit polarization; for example, in surface waves in liquids (gravity waves), the wave displacement of the particles is always in a vertical plane.

Light or other electromagnetic radiation from many sources, such as the sun, flames, and incandescent lamps, consists of short wave trains with an equal mixture of polarizations; this is called unpolarized light. Polarized light can be produced by passing unpolarized light through a polarizing filter, which allows waves of only one polarization to pass through, the most common optical materials (such as glass) are isotropic and do not affect the polarization of light passing through them; however, some materials—those that exhibit birefringence, dichroism, or optical activity—can change the polarization of light. Some of these are used to make polarizing filters. Light is also partially polarized when it reflects from a surface.

According to quantum mechanics, electromagnetic waves can also be viewed as streams of particles called photons. When viewed in this way, the polarization of an electromagnetic wave is determined by a quantum mechanical property of photons called their spin. A photon has one of two possible spins: it can either spin in a right hand sense or a left hand sense about its direction of travel. Circularly polarized electromagnetic waves are composed of photons with only one type of spin, either right- or left-hand. Linearly polarized waves consist of equal numbers of right and left hand spinning photons, with their phase synchronized so they superpose to give oscillation in a plane.

Most sources of light are classified as incoherent and unpolarized (or only "partially polarized") because they consist of a random mixture of waves having different spatial characteristics, frequencies (wavelengths), phases, and polarization states. However, for understanding electromagnetic waves and polarization in particular, it is easiest to just consider coherent plane waves; these are sinusoidal waves of one particular direction (or wavevector), frequency, phase, and polarization state. Characterizing an optical system in relation to a plane wave with those given parameters can then be used to predict its response to a more general case, since a wave with any specified spatial structure can be decomposed into a combination of plane waves (its so-called angular spectrum). And incoherent states can be modeled stochastically as a weighted combination of such uncorrelated waves with some distribution of frequencies (its spectrum), phases, and polarizations.

A "vertically polarized" electromagnetic wave of wavelength λ has its electric field vector E (red) oscillating in the vertical direction. The magnetic field B (or H) is always at right angles to it (blue), and both are perpendicular to the direction of propagation (z).

Electromagnetic waves (such as light), traveling in free space or another homogeneousisotropicnon-attenuating medium, are properly described as transverse waves, meaning that a plane wave's electric field vector E and magnetic field H are in directions perpendicular to (or "transverse" to) the direction of wave propagation; E and H are also perpendicular to each other. Considering a monochromatic plane wave of optical frequency f (light of vacuum wavelength λ has a frequency of f = c/λ where c is the speed of light), let us take the direction of propagation as the z axis. Being a transverse wave the E and H fields must then contain components only in the x and y directions whereas Ez=Hz=0. Using complex (or phasor) notation, we understand the instantaneous physical electric and magnetic fields to be given by the real parts of the complex quantities occurring in the following equations. As a function of time t and spatial position z (since for a plane wave in the +z direction the fields have no dependence on x or y) these complex fields can be written as:

where λ/n is the wavelength in the medium (whose refractive index is n) and T = 1/f is the period of the wave. Here ex, ey, hx, and hy are complex numbers. In the second more compact form, as these equations are customarily expressed, these factors are described using the wavenumberk=2πn/λ{\displaystyle k=2\pi n/\lambda } and angular frequency (or "radian frequency") ω=2πf{\displaystyle \omega =2\pi f}. In a more general formulation with propagation not restricted to the +z direction, then the spatial dependence kz is replaced by k→⋅r→{\displaystyle {\vec {k}}\cdot {\vec {r}}} where k→{\displaystyle {\vec {k}}} is called the wave vector, the magnitude of which is the wavenumber.

Thus the leading vectors e and h each contain up to two nonzero (complex) components describing the amplitude and phase of the wave's x and y polarization components (again, there can be no z polarization component for a transverse wave in the +z direction). For a given medium with a characteristic impedanceη{\displaystyle \eta }, h is related to e by:

hy=ex/η{\displaystyle h_{y}=e_{x}/\eta }

and

hx=−ey/η{\displaystyle h_{x}=-e_{y}/\eta } .

In a dielectric, η is real and has the value η0/n, where n is the refractive index and η0 is the impedance of free space. The impedance will be complex in a conducting medium.[clarification needed] Note that given that relationship, the dot product of E and H must be zero:[dubious– discuss]

indicating that these vectors are orthogonal (at right angles to each other), as expected.

So knowing the propagation direction (+z in this case) and η, one can just as well specify the wave in terms of just ex and ey describing the electric field. The vector containing ex and ey (but without the z component which is necessarily zero for a transverse wave) is known as a Jones vector. In addition to specifying the polarization state of the wave, a general Jones vector also specifies the overall magnitude and phase of that wave. Specifically, the intensity of the light wave is proportional to the sum of the squared magnitudes of the two electric field components:

however the wave's state of polarization is only dependent on the (complex) ratio of ey to ex. So let us just consider waves whose |ex|2 + |ey|2 = 1; this happens to correspond to an intensity of about .00133 watts per square meter in free space (where η={\displaystyle \eta =}η0{\displaystyle \eta _{0}}). And since the absolute phase of a wave is unimportant in discussing its polarization state, let us stipulate that the phase of ex is zero, in other words ex is a real number while ey may be complex. Under these restrictions, ex and ey can be represented as follows:

ex=1+Q2{\displaystyle e_{x}={\sqrt {\frac {1+Q}{2}}}}

ey=1−Q2eiϕ{\displaystyle e_{y}={\sqrt {\frac {1-Q}{2}}}\,e^{i\phi }}

where the polarization state is now fully parameterized by the value of Q (such that −1 < Q < 1) and the relative phase ϕ{\displaystyle \phi }. By convention when one speaks of a wave's "polarization," if not otherwise specified, reference is being made to the polarization of the electric field, the polarization of the magnetic field always follows that of the electric field but with a 90 degree rotation, as detailed above.

In addition to transverse waves, there are many wave motions where the oscillation is not limited to directions perpendicular to the direction of propagation, these cases are far beyond the scope of the current article which concentrates on transverse waves (such as most electromagnetic waves in bulk media), however one should be aware of cases where the polarization of a coherent wave cannot be described simply using a Jones vector, as we have just done.

Even in free space, longitudinal field components can be generated in focal regions, where the plane wave approximation breaks down. An extreme example is radially or tangentially polarized light, at the focus of which the electric or magnetic field respectively is entirely longitudinal (along the direction of propagation).[9]

For longitudinal waves such as sound waves in fluids, the direction of oscillation is by definition along the direction of travel, so the issue of polarization is not normally even mentioned. On the other hand, sound waves in a bulk solid can be transverse as well as longitudinal, for a total of three polarization components; in this case, the transverse polarization is associated with the direction of the shear stress and displacement in directions perpendicular to the propagation direction, while the longitudinal polarization describes compression of the solid and vibration along the direction of propagation. The differential propagation of transverse and longitudinal polarizations is important in seismology.

Polarization is best understood by initially considering only pure polarization states, and only a coherent sinusoidal wave at some optical frequency, the vector in the adjacent diagram might describe the oscillation of the electric field emitted by a single-mode laser (whose oscillation frequency would be typically 1015 times faster). The field oscillates in the x-y plane, along the page, with the wave propagating in the z direction, perpendicular to the page, the first two diagrams below trace the electric field vector over a complete cycle for linear polarization at two different orientations; these are each considered a distinct state of polarization (SOP). Note that the linear polarization at 45° can also be viewed as the addition of a horizontally linearly polarized wave (as in the leftmost figure) and a vertically polarized wave of the same amplitude in the same phase.

Animation showing four different polarization states and two orthogonal projections.

A circularly polarized wave as a sum of two linearly polarized components 90° out of phase

Now if one were to introduce a phase shift in between those horizontal and vertical polarization components, one would generally obtain elliptical polarization[10] as is shown in the third figure. When the phase shift is exactly ±90°, then circular polarization is produced (fourth and fifth figures), thus is circular polarization created in practice, starting with linearly polarized light and employing a quarter-wave plate to introduce such a phase shift. The result of two such phase-shifted components in causing a rotating electric field vector is depicted in the animation on the right. Note that circular or elliptical polarization can involve either a clockwise or counterclockwise rotation of the field, these correspond to distinct polarization states, such as the two circular polarizations shown above.

Of course the orientation of the x and y axes used in this description is arbitrary, the choice of such a coordinate system and viewing the polarization ellipse in terms of the x and y polarization components, corresponds to the definition of the Jones vector (below) in terms of those basis polarizations. One would typically choose axes to suit a particular problem such as x being in the plane of incidence, since there are separate reflection coefficients for the linear polarizations in and orthogonal to the plane of incidence (p and s polarizations, see below), that choice greatly simplifies the calculation of a wave's reflection from a surface.

Moreover, one can use as basis functions any pair of orthogonal polarization states, not just linear polarizations, for instance, choosing right and left circular polarizations as basis functions simplifies the solution of problems involving circular birefringence (optical activity) or circular dichroism.

Consider a purely polarized monochromatic wave. If one were to plot the electric field vector over one cycle of oscillation, an ellipse would generally be obtained, as is shown in the figure, corresponding to a particular state of elliptical polarization. Note that linear polarization and circular polarization can be seen as special cases of elliptical polarization.

A polarization state can then be described in relation to the geometrical parameters of the ellipse, and its "handedness", that is, whether the rotation around the ellipse is clockwise or counter clockwise. One parameterization of the elliptical figure specifies the orientation angle ψ, defined as the angle between the major axis of the ellipse and the x-axis[11] along with the ellipticity ε=a/b, the ratio of the ellipse's major to minor axis.[12][13][14][15] (also known as the axial ratio). The ellipticity parameter is an alternative parameterization of an ellipse's eccentricitye=1−b2/a2{\displaystyle e={\sqrt {1-b^{2}/a^{2}}}}, or the ellipticity angle, χ = arctan b/a= arctan 1/ε as is shown in the figure.[11] The angle χ is also significant in that the latitude (angle from the equator) of the polarization state as represented on the Poincaré sphere (see below) is equal to ±2χ, the special cases of linear and circular polarization correspond to an ellipticity ε of infinity and unity (or χ of zero and 45°) respectively.

Full information on a completely polarized state is also provided by the amplitude and phase of oscillations in two components of the electric field vector in the plane of polarization, this representation was used above to show how different states of polarization are possible. The amplitude and phase information can be conveniently represented as a two-dimensional complex vector (the Jones vector):

Here a1{\displaystyle a_{1}} and a2{\displaystyle a_{2}} denote the amplitude of the wave in the two components of the electric field vector, while θ1{\displaystyle \theta _{1}} and θ2{\displaystyle \theta _{2}} represent the phases. The product of a Jones vector with a complex number of unit modulus gives a different Jones vector representing the same ellipse, and thus the same state of polarization, the physical electric field, as the real part of the Jones vector, would be altered but the polarization state itself is independent of absolute phase. The basis vectors used to represent the Jones vector need not represent linear polarization states (i.e. be real). In general any two orthogonal states can be used, where an orthogonal vector pair is formally defined as one having a zero inner product. A common choice is left and right circular polarizations, for example to model the different propagation of waves in two such components in circularly birefringent media (see below) or signal paths of coherent detectors sensitive to circular polarization.

Regardless of whether polarization state is represented using geometric parameters or Jones vectors, implicit in the parameterization is the orientation of the coordinate frame, this permits a degree of freedom, namely rotation about the propagation direction. When considering light that is propagating parallel to the surface of the Earth, the terms "horizontal" and "vertical" polarization are often used, with the former being associated with the first component of the Jones vector, or zero azimuth angle, on the other hand, in astronomy the equatorial coordinate system is generally used instead, with the zero azimuth (or position angle, as it is more commonly called in astronomy to avoid confusion with the horizontal coordinate system) corresponding to due north.

Electromagnetic vectors for E{\textstyle {\textbf {E}}}, B{\textstyle {\textbf {B}}} and k{\textstyle {\textbf {k}}} with E=E(x,y){\textstyle {\textbf {E}}={\textbf {E}}(x,y)} along with 3 planar projections and a deformation surface of total electric field. The light is always s-polarized in the xy plane. θ{\textstyle \theta } is the polar angle of k{\textstyle {\textbf {k}}} and φE{\textstyle \varphi _{E}} is the azimuthal angle of E{\textstyle {\textbf {E}}}.

Another coordinate system frequently used relates to the plane of incidence, this is the plane made by the incoming propagation direction and the vector perpendicular to the plane of an interface, in other words, the plane in which the ray travels before and after reflection or refraction. The component of the electric field parallel to this plane is termed p-like (parallel) and the component perpendicular to this plane is termed s-like (from senkrecht, German for perpendicular). Polarized light with its electric field along the plane of incidence is thus denoted p-polarized, while light whose electric field is normal to the plane of incidence is called s-polarized. P polarization is commonly referred to as transverse-magnetic (TM), and has also been termed pi-polarized or tangential plane polarized. S polarization is also called transverse-electric (TE), as well as sigma-polarized or sagittal plane polarized.

Natural light, and most other common sources of visible light, are incoherent: radiation is produced independently by a large number of atoms or molecules whose emissions are uncorrelated and generally of random polarizations; in this case the light is said to be unpolarized. This term is somewhat inexact, since at any instant of time at one location there is a definite direction to the electric and magnetic fields, however it implies that the polarization changes so quickly in time that it will not be measured or relevant to the outcome of an experiment. A so-called depolarizer acts on a polarized beam to create one which is actually fully polarized at every point, but in which the polarization varies so rapidly across the beam that it may be ignored in the intended applications.

Unpolarized light can be described as a mixture of two independent oppositely polarized streams, each with half the intensity.[16][17] Light is said to be partially polarized when there is more power in one of these streams than the other, at any particular wavelength, partially polarized light can be statistically described as the superposition of a completely unpolarized component and a completely polarized one.[18]:330 One may then describe the light in terms of the degree of polarization and the parameters of the polarized component, that polarized component can be described in terms of a Jones vector or polarization ellipse, as is detailed above. However, in order to also describe the degree of polarization, one normally employs Stokes parameters (see below) to specify a state of partial polarization.[18]:351,374–375

The transmission of plane waves through a homogeneous medium are fully described in terms of Jones vectors and 2×2 Jones matrices. However, in practice there are cases in which all of the light cannot be viewed in such a simple manner due to spatial inhomogeneities or the presence of mutually incoherent waves. So-called depolarization, for instance, cannot be described using Jones matrices, for these cases it is usual instead to use a 4×4 matrix that acts upon the Stokes 4-vector. Such matrices were first used by Paul Soleillet in 1929, although they have come to be known as Mueller matrices. While every Jones matrix has a Mueller matrix, the reverse is not true. Mueller matrices are then used to describe the observed polarization effects of the scattering of waves from complex surfaces or ensembles of particles, as shall now be presented.[18]:377–379

The Jones vector perfectly describes the state of polarization and phase of a single monochromatic wave, representing a pure state of polarization as described above, however any mixture of waves of different polarizations (or even of different frequencies) do not correspond to a Jones vector. In so-called partially polarized radiation the fields are stochastic, and the variations and correlations between components of the electric field can only be described statistically. One such representation is the coherency matrix:[19]:137–142

where angular brackets denote averaging over many wave cycles. Several variants of the coherency matrix have been proposed: the Wiener coherency matrix and the spectral coherency matrix of Richard Barakat measure the coherence of a spectral decomposition of the signal, while the Wolf coherency matrix averages over all time/frequencies.

The coherency matrix contains all second order statistical information about the polarization, this matrix can be decomposed into the sum of two idempotent matrices, corresponding to the eigenvectors of the coherency matrix, each representing a polarization state that is orthogonal to the other. An alternative decomposition is into completely polarized (zero determinant) and unpolarized (scaled identity matrix) components; in either case, the operation of summing the components corresponds to the incoherent superposition of waves from the two components. The latter case gives rise to the concept of the "degree of polarization"; i.e., the fraction of the total intensity contributed by the completely polarized component.

The coherency matrix is not easy to visualize, and it is therefore common to describe incoherent or partially polarized radiation in terms of its total intensity (I), (fractional) degree of polarization (p), and the shape parameters of the polarization ellipse. An alternative and mathematically convenient description is given by the Stokes parameters, introduced by George Gabriel Stokes in 1852, the relationship of the Stokes parameters to intensity and polarization ellipse parameters is shown in the equations and figure below.

S0=I{\displaystyle S_{0}=I\,}

S1=Ipcos⁡2ψcos⁡2χ{\displaystyle S_{1}=Ip\cos 2\psi \cos 2\chi \,}

S2=Ipsin⁡2ψcos⁡2χ{\displaystyle S_{2}=Ip\sin 2\psi \cos 2\chi \,}

S3=Ipsin⁡2χ{\displaystyle S_{3}=Ip\sin 2\chi \,}

Here Ip, 2ψ and 2χ are the spherical coordinates of the polarization state in the three-dimensional space of the last three Stokes parameters. Note the factors of two before ψ and χ corresponding respectively to the facts that any polarization ellipse is indistinguishable from one rotated by 180°, or one with the semi-axis lengths swapped accompanied by a 90° rotation, the Stokes parameters are sometimes denoted I, Q, U and V.

Neglecting the first Stokes parameter S0 (or I), the three other Stokes parameters can be plotted directly in three-dimensional Cartesian coordinates. For a given power in the polarized component given by

The normalized Stokes vector S′{\displaystyle \mathbf {S'} } then has unity power (S0′=1{\displaystyle S'_{0}=1}) and the three significant Stokes parameters plotted in three dimensions will lie on the unity-radius Poincaré sphere for pure polarization states (where P0′=1{\displaystyle P'_{0}=1}). Partially polarized states will lie inside the Poincaré sphere at a distance of P′=S1′2+S2′2+S3′2{\displaystyle P'={\sqrt {S_{1}'^{2}+S_{2}'^{2}+S_{3}'^{2}}}} from the origin. When the non-polarized component is not of interest, the Stokes vector can be further normalized to obtain

When plotted, that point will lie on the surface of the unity-radius Poincaré sphere and indicate the state of polarization of the polarized component.

Any two antipodal points on the Poincaré sphere refer to orthogonal polarization states, the overlap between any two polarization states is dependent solely on the distance between their locations along the sphere. This property, which can only be true when pure polarization states are mapped onto a sphere, is the motivation for the invention of the Poincaré sphere and the use of Stokes parameters, which are thus plotted on (or beneath) it.

In a vacuum, the components of the electric field propagate at the speed of light, so that the phase of the wave varies in space and time while the polarization state does not, that is, the electric field vector e of a plane wave in the +z direction follows:

where k is the wavenumber. As noted above, the instantaneous electric field is the real part of the product of the Jones vector times the phase factor e−iωt{\displaystyle e^{-i\omega t}}. When an electromagnetic wave interacts with matter, its propagation is altered according to the material's (complex) index of refraction. When the real or imaginary part of that refractive index is dependent on the polarization state of a wave, properties known as birefringence and polarization dichroism (or diattenuation) respectively, then the polarization state of a wave will generally be altered.

In such media, an electromagnetic wave with any given state of polarization may be decomposed into two orthogonally polarized components that encounter different propagation constants, the effect of propagation over a given path on those two components is most easily characterized in the form of a complex 2×2 transformation matrix J known as a Jones matrix:

e′=Je.{\displaystyle \mathbf {e'} =\mathbf {J} \mathbf {e} .}

The Jones matrix due to passage through a transparent material is dependent on the propagation distance as well as the birefringence, the birefringence (as well as the average refractive index) will generally be dispersive, that is, it will vary as a function of optical frequency (wavelength). In the case of non-birefringent materials, however, the 2×2 Jones matrix is the identity matrix (multiplied by a scalar phase factor and attenuation factor), implying no change in polarization during propagation.

For propagation effects in two orthogonal modes, the Jones matrix can be written as

where g1 and g2 are complex numbers describing the phase delay and possibly the amplitude attenuation due to propagation in each of the two polarization eigenmodes. T is a unitary matrix representing a change of basis from these propagation modes to the linear system used for the Jones vectors; in the case of linear birefringence or diattenuation the modes are themselves linear polarization states so T and T−1 can be omitted if the coordinate axes have been chosen appropriately.

In media termed birefringent, in which the amplitudes are unchanged but a differential phase delay occurs, the Jones matrix is a unitary matrix: |g1| = |g2| = 1. Media termed diattenuating (or dichroic in the sense of polarization), in which only the amplitudes of the two polarizations are affected differentially, may be described using a Hermitian matrix (generally multiplied by a common phase factor); in fact, since any matrix may be written as the product of unitary and positive Hermitian matrices, light propagation through any sequence of polarization-dependent optical components can be written as the product of these two basic types of transformations.

In birefringent media there is no attenuation, but two modes accrue a differential phase delay. Well known manifestations of linear birefringence (that is, in which the basis polarizations are orthogonal linear polarizations) appear in optical wave plates/retarders and many crystals. If linearly polarized light passes through a birefringent material, its state of polarization will generally change, unless its polarization direction is identical to one of those basis polarizations, since the phase shift, and thus the change in polarization state, is usually wavelength-dependent, such objects viewed under white light in between two polarizers may give rise to colorful effects, as seen in the accompanying photograph.

Circular birefringence is also termed optical activity, especially in chiral fluids, or Faraday rotation, when due to the presence of a magnetic field along the direction of propagation. When linearly polarized light is passed through such an object, it will exit still linearly polarized, but with the axis of polarization rotated. A combination of linear and circular birefringence will have as basis polarizations two orthogonal elliptical polarizations; however, the term "elliptical birefringence" is rarely used.

Paths taken by vectors in the Poincaré sphere under birefringence. The propagation modes (rotation axes) are shown with red, blue, and yellow lines, the initial vectors by thick black lines, and the paths they take by colored ellipses (which represent circles in three dimensions).

One can visualize the case of linear birefringence (with two orthogonal linear propagation modes) with an incoming wave linearly polarized at a 45° angle to those modes, as a differential phase starts to accrue, the polarization becomes elliptical, eventually changing to purely circular polarization (90° phase difference), then to elliptical and eventually linear polarization (180° phase) perpendicular to the original polarization, then through circular again (270° phase), then elliptical with the original azimuth angle, and finally back to the original linearly polarized state (360° phase) where the cycle begins anew. In general the situation is more complicated and can be characterized as a rotation in the Poincaré sphere about the axis defined by the propagation modes. Examples for linear (blue), circular (red), and elliptical (yellow) birefringence are shown in the figure on the left, the total intensity and degree of polarization are unaffected. If the path length in the birefringent medium is sufficient, the two polarization components of a collimated beam (or ray) can exit the material with a positional offset, even though their final propagation directions will be the same (assuming the entrance face and exit face are parallel), this is commonly viewed using calcitecrystals, which present the viewer with two slightly offset images, in opposite polarizations, of an object behind the crystal. It was this effect that provided the first discovery of polarization, by Erasmus Bartholinus in 1669.

Media in which transmission of one polarization mode is preferentially reduced are called dichroic or diattenuating. Like birefringence, diattenuation can be with respect to linear polarization modes (in a crystal) or circular polarization modes (usually in a liquid).

Devices that block nearly all of the radiation in one mode are known as polarizing filters or simply "polarizers", this corresponds to g2=0 in the above representation of the Jones matrix. The output of an ideal polarizer is a specific polarization state (usually linear polarization) with an amplitude equal to the input wave's original amplitude in that polarization mode. Power in the other polarization mode is eliminated, thus if unpolarized light is passed through an ideal polarizer (where g1=1 and g2=0) exactly half of its initial power is retained. Practical polarizers, especially inexpensive sheet polarizers, have additional loss so that g1 < 1. However, in many instances the more relevant figure of merit is the polarizer's degree of polarization or extinction ratio, which involve a comparison of g1 to g2. Since Jones vectors refer to waves' amplitudes (rather than intensity), when illuminated by unpolarized light the remaining power in the unwanted polarization will be (g2/g1)2 of the power in the intended polarization.

In addition to birefringence and dichroism in extended media, polarization effects describable using Jones matrices can also occur at (reflective) interface between two materials of different refractive index, these effects are treated by the Fresnel equations. Part of the wave is transmitted and part is reflected; for a given material those proportions (and also the phase of reflection) are dependent on the angle of incidence and are different for the s and p polarizations. Therefore, the polarization state of reflected light (even if initially unpolarized) is generally changed.

A stack of plates at Brewster's angle to a beam reflects off a fraction of the s-polarized light at each surface, leaving (after many such plates) a mainly p-polarized beam.

Any light striking a surface at a special angle of incidence known as Brewster's angle, where the reflection coefficient for p polarization is zero, will be reflected with only the s-polarization remaining. This principle is employed in the so-called "pile of plates polarizer" (see figure) in which part of the s polarization is removed by reflection at each Brewster angle surface, leaving only the p polarization after transmission through many such surfaces. The generally smaller reflection coefficient of the p polarization is also the basis of polarized sunglasses; by blocking the s (horizontal) polarization, most of the glare due to reflection from a wet street, for instance, is removed.[18]:348–350

In the important special case of reflection at normal incidence (not involving anisotropic materials) there is no particular s or p polarization. Both the x and y polarization components are reflected identically, and therefore the polarization of the reflected wave is identical to that of the incident wave. However, in the case of circular (or elliptical) polarization, the handedness of the polarization state is thereby reversed, since by convention this is specified relative to the direction of propagation, the circular rotation of the electric field around the x-y axes called "right-handed" for a wave in the +z direction is "left-handed" for a wave in the -z direction. But in the general case of reflection at a nonzero angle of incidence, no such generalization can be made, for instance, right-circularly polarized light reflected from a dielectric surface at a grazing angle, will still be right-handed (but elliptically) polarized. Linear polarized light reflected from a metal at non-normal incidence will generally become elliptically polarized, these cases are handled using Jones vectors acted upon by the different Fresnel coefficients for the s and p polarization components.

Some optical measurement techniques are based on polarization; in many other optical techniques polarization is crucial or at least must be taken into account and controlled; such examples are too numerous to mention.

In engineering, the phenomenon of stress induced birefringence allows for stresses in transparent materials to be readily observed, as noted above and seen in the accompanying photograph, the chromaticity of birefringence typically creates colored patterns when viewed in between two polarizers. As external forces are applied, internal stress induced in the material is thereby observed. Additionally, birefringence is frequently observed due to stresses "frozen in" at the time of manufacture, this is famously observed in cellophane tape whose birefringence is due to the stretching of the material during the manufacturing process.

Ellipsometry is a powerful technique for the measurement of the optical properties of a uniform surface, it involves measuring the polarization state of light following specular reflection from such a surface. This is typically done as a function of incidence angle or wavelength (or both), since ellipsometry relies on reflection, it is not required for the sample to be transparent to light or for its back side to be accessible.

Ellipsometry can be used to model the (complex) refractive index of a surface of a bulk material, it is also very useful in determining parameters of one or more thin film layers deposited on a substrate. Due to their reflection properties, not only are the predicted magnitude of the p and s polarization components, but their relative phase shifts upon reflection, compared to measurements using an ellipsometer. A normal ellipsometer does not measure the actual reflection coefficient (which requires careful photometric calibration of the illuminating beam) but the ratio of the p and s reflections, as well as change of polarization ellipticity (hence the name) induced upon reflection by the surface being studied. In addition to use in science and research, ellipsometers are used in situ to control production processes for instance.[20]:585ff[21]:632

The property of (linear) birefringence is widespread in crystalline minerals, and indeed was pivotal in the initial discovery of polarization; in mineralogy, this property is frequently exploited using polarization microscopes, for the purpose of identifying minerals. See optical mineralogy for more details.[22]:163–164

Sound waves in solid materials exhibit polarization. Differential propagation of the three polarizations through the earth is a crucial in the field of seismology. Horizontally and vertically polarized seismic waves (shear waves)are termed SH and SV, while waves with longitudinal polarization (compressional waves) are termed P-waves.[23]:48–50[24]:56–57

We have seen (above) that the birefringence of a type of crystal is useful in identifying it, and thus detection of linear birefringence is especially useful in geology and mineralogy. Linearly polarized light generally has its polarization state altered upon transmission through such a crystal, making it stand out when viewed in between two crossed polarizers, as seen in the photograph, above. Likewise, in chemistry, rotation of polarization axes in a liquid solution can be a useful measurement; in a liquid, linear birefringence is impossible, however there may be circular birefringence when a chiral molecule is in solution. When the right and left handed enantiomers of such a molecule are present in equal numbers (a so-called racemic mixture) then their effects cancel out. However, when there is only one (or a preponderance of one), as is more often the case for organic molecules, a net circular birefringence (or optical activity) is observed, revealing the magnitude of that imbalance (or the concentration of the molecule itself, when it can be assumed that only one enantiomer is present). This is measured using a polarimeter in which polarized light is passed through a tube of the liquid, at the end of which is another polarizer which is rotated in order to null the transmission of light through it.[18]:360–365[25]:169–172

In many areas of astronomy, the study of polarized electromagnetic radiation from outer space is of great importance, although not usually a factor in the thermal radiation of stars, polarization is also present in radiation from coherent astronomical sources (e.g. hydroxyl or methanol masers), and incoherent sources such as the large radio lobes in active galaxies, and pulsar radio radiation (which may, it is speculated, sometimes be coherent), and is also imposed upon starlight by scattering from interstellar dust. Apart from providing information on sources of radiation and scattering, polarization also probes the interstellar magnetic field via Faraday rotation.[26]:119,124[27]:336–337 The polarization of the cosmic microwave background is being used to study the physics of the very early universe.[28][29]Synchrotron radiation is inherently polarised. It has been suggested that astronomical sources caused the chirality of biological molecules on Earth.[30]

Effect of a polarizer on reflection from mud flats. In the picture on the left, the horizontally oriented polarizer preferentially transmits those reflections; rotating the polarizer by 90° (right) as one would view using polarized sunglasses blocks almost all specularly reflected sunlight.

Unpolarized light, after being reflected by a specular (shiny) surface, generally obtains a degree of polarization, this phenomenon was observed in 1808 by the mathematician Étienne-Louis Malus, after whom Malus's law is named. Polarizing sunglasses exploit this effect to reduce glare from reflections by horizontal surfaces, notably the road ahead viewed at a grazing angle.

Wearers of polarized sunglasses will occasionally observe inadvertent polarization effects such as color-dependent birefringent effects, for example in toughened glass (e.g., car windows) or items made from transparent plastics, in conjunction with natural polarization by reflection or scattering. The polarized light from LCD monitors (see below) is very conspicuous when these are worn.

Polarization is observed in the light of the sky, as this is due to sunlight scattered by aerosols as it passes through the earth's atmosphere, the scattered light produces the brightness and color in clear skies. This partial polarization of scattered light can be used to darken the sky in photographs, increasing the contrast, this effect is most strongly observed at points on the sky making a 90° angle to the sun. Polarizing filters use these effects to optimize the results of photographing scenes in which reflection or scattering by the sky is involved.[18]:346–347[31]:495–499

The principle of liquid-crystal display (LCD) technology relies on the rotation of the axis of linear polarization by the liquid crystal array. Light from the backlight (or the back reflective layer, in devices not including or requiring a backlight) first passes through a linear polarizing sheet, that polarized light passes through the actual liquid crystal layer which may be organized in pixels (for a TV or computer monitor) or in another format such as a seven-segment display or one with custom symbols for a particular product. The liquid crystal layer is produced with a consistent right (or left) handed chirality, essentially consisting of tiny helices, this causes circular birefringence, and is engineered so that there is a 90 degree rotation of the linear polarization state. However, when a voltage is applied across a cell, the molecules straighten out, lessening or totally losing the circular birefringence, on the viewing side of the display is another linear polarizing sheet, usually oriented at 90 degrees from the one behind the active layer. Therefore, when the circular birefringence is removed by the application of a sufficient voltage, the polarization of the transmitted light remains at right angles to the front polarizer, and the pixel appears dark, with no voltage, however, the 90 degree rotation of the polarization causes it to exactly match the axis of the front polarizer, allowing the light through. Intermediate voltages create intermediate rotation of the polarization axis and the pixel has an intermediate intensity. Displays based on this principle are widespread, and now are used in the vast majority of televisions, computer monitors and video projectors, rendering the previous CRT technology essentially obsolete, the use of polarization in the operation of LCD displays is immediately apparent to someone wearing polarized sunglasses, often making the display unreadable.

In a totally different sense, polarization encoding has become the leading (but not sole) method for delivering separate images to the left and right eye in stereoscopic displays used for 3D movies, this involves separate images intended for each eye either projected from two different projectors with orthogonally oriented polarizing filters or, more typically, from a single projector with time multiplexed polarization (a fast alternating polarization device for successive frames). Polarized 3D glasses with suitable polarizing filters ensure that each eye receives only the intended image. Historically such systems used linear polarization encoding because it was inexpensive and offered good separation, however circular polarization makes separation of the two images insensitive to tilting of the head, and is widely used in 3-D movie exhibition today, such as the system from RealD. Projecting such images requires screens that maintain the polarization of the projected light when viewed in reflection (such as silver screens); a normal diffuse white projection screen causes depolarization of the projected images, making it unsuitable for this application.

Although now obsolete, CRT computer displays suffered from reflection by the glass envelope, causing glare from room lights and consequently poor contrast. Several anti-reflection solutions were employed to ameliorate this problem. One solution utilized the principle of reflection of circularly polarized light. A circular polarizing filter in front of the screen allows for the transmission of (say) only right circularly polarized room light. Now, right circularly polarized light (depending on the convention used) has its electric (and magnetic) field direction rotating clockwise while propagating in the +z direction. Upon reflection, the field still has the same direction of rotation, but now propagation is in the −z direction making the reflected wave left circularly polarized, with the right circular polarization filter placed in front of the reflecting glass, the unwanted light reflected from the glass will thus be in very polarization state that is blocked by that filter, eliminating the reflection problem. The reversal of circular polarization on reflection and elimination of reflections in this manner can be easily observed by looking in a mirror while wearing 3-D movie glasses which employ left- and right-handed circular polarization in the two lenses. Closing one eye, the other eye will see a reflection in which it cannot see itself; that lens appears black. However the other lens (of the closed eye) will have the correct circular polarization allowing the closed eye to be easily seen by the open one.

All radio (and microwave) antennas used for transmitting or receiving are intrinsically polarized, they transmit in (or receive signals from) a particular polarization, being totally insensitive to the opposite polarization; in certain cases that polarization is a function of direction. Most antennas are nominally linearly polarized, but elliptical and circular polarization is a possibility, as is the convention in optics, the "polarization" of a radio wave is understood to refer to the polarization of its electric field, with the magnetic field being at a 90 degree rotation with respect to it for a linearly polarized wave.

The vast majority of antennas are linearly polarized; in fact it can be shown from considerations of symmetry that an antenna that lies entirely in a plane which also includes the observer, can only have its polarization in the direction of that plane. This applies to many cases, allowing one to easily infer such an antenna's polarization at an intended direction of propagation. So a typical rooftop Yagi or log-periodic antenna with horizontal conductors, as viewed from a second station toward the horizon, is necessarily horizontally polarized, but a vertical "whip antenna" or AM broadcast tower used as an antenna element (again, for observers horizontally displaced from it) will transmit in the vertical polarization. A turnstile antenna with its four arms in the horizontal plane, likewise transmits horizontally polarized radiation toward the horizon. However, when that same turnstile antenna is used in the "axial mode" (upwards, for the same horizontally-oriented structure) its radiation is circularly polarized, at intermediate elevations it is elliptically polarized.

Polarization is important in radio communications because, for instance, if one attempts to use a horizontally polarized antenna to receive a vertically polarized transmission, the signal strength will be substantially reduced (or under very controlled conditions, reduced to nothing), this principle is used in satellite television in order to double the channel capacity over a fixed frequency band. The same frequency channel can be used for two signals broadcast in opposite polarizations. By adjusting the receiving antenna for one or the other polarization, either signal can be selected without interference from the other.

Especially due to the presence of the ground, there are some differences in propagation (and also in reflections responsible for TV ghosting) between horizontal and vertical polarizations. AM and FM broadcast radio usually use vertical polarization, while television uses horizontal polarization, at low frequencies especially, horizontal polarization is avoided. That is because the phase of a horizontally polarized wave is reversed upon reflection by the ground. A distant station in the horizontal direction will receive both the direct and reflected wave, which thus tend to cancel each other, this problem is avoided with vertical polarization. Polarization is also important in the transmission of radar pulses and reception of radar reflections by the same or a different antenna, for instance, back scattering of radar pulses by rain drops can be avoided by using circular polarization. Just as specular reflection of circularly polarized light reverses the handedness of the polarization, as discussed above, the same principle applies to scattering by objects much smaller than a wavelength such as rain drops, on the other hand, reflection of that wave by an irregular metal object (such as an airplane) will typically introduce a change in polarization and (partial) reception of the return wave by the same antenna.

The effect of free electrons in the ionosphere, in conjunction with the earth's magnetic field, causes Faraday rotation, a sort of circular birefringence. This is the same mechanism which can rotate the axis of linear polarization by electrons in interstellar space as mentioned below, the magnitude of Faraday rotation caused by such a plasma is greatly exaggerated at lower frequencies, so at the higher microwave frequencies used by satellites the effect is minimal. However medium or short wave transmissions received following refraction by the ionosphere are strongly affected, since a wave's path through the ionosphere and the earth's magnetic field vector along such a path are rather unpredictable, a wave transmitted with vertical (or horizontal) polarization will generally have a resulting polarization in an arbitrary orientation at the receiver.

Many animals are capable of perceiving some of the components of the polarization of light, e.g., linear horizontally polarized light. This is generally used for navigational purposes, since the linear polarization of sky light is always perpendicular to the direction of the sun, this ability is very common among the insects, including bees, which use this information to orient their communicative dances.[32]:102–103 Polarization sensitivity has also been observed in species of octopus, squid, cuttlefish, and mantis shrimp.[32]:111–112 In the latter case, one species measures all six orthogonal components of polarization, and is believed to have optimal polarization vision,[33] the rapidly changing, vividly colored skin patterns of cuttlefish, used for communication, also incorporate polarization patterns, and mantis shrimp are known to have polarization selective reflective tissue. Sky polarization was thought to be perceived by pigeons, which was assumed to be one of their aids in homing, but research indicates this is a popular myth.[34]

The naked human eye is weakly sensitive to polarization, without the need for intervening filters. Polarized light creates a very faint pattern near the center of the visual field, called Haidinger's brush, this pattern is very difficult to see, but with practice one can learn to detect polarized light with the naked eye.[32]:118

It is well known that electromagnetic radiation carries a certain linear momentum in the direction of propagation; in addition, however, light carries a certain angular momentum if it is circularly polarized (or partially so). In comparison with lower frequencies such as microwaves, the amount of angular momentum in light, even of pure circular polarization, compared to the same wave's linear momentum (or radiation pressure) is very small and difficult to even measure, however it was utilized in an experiment to achieve speeds of up to 600 million revolutions per minute.[35][36]

^John Volakis (ed) 2007 Antenna Engineering Handbook, Fourth Edition, sec. 26.1. Note: in contrast with other authors, this source initially defines ellipticity reciprocally, as the minor-to-major-axis ratio, but then goes on to say that "Although [it] is less than unity, when expressing ellipticity in decibels, the minus sign is frequently omitted for convenience", which essentially reverts back to the definition adopted by other authors.

1.
American and British English spelling differences
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Many of the differences between American and British English date back to a time when spelling standards had not yet developed. For instance, some spellings seen as American today were once used in Britain. But English-language spelling reform has rarely been adopted otherwise, and thus modern English orthography varies somewhat between countries and is far from phonemic in any country, in the early 18th century, English spelling was inconsistent. These differences became noticeable after the publishing of influential dictionaries, todays British English spellings mostly follow Johnsons A Dictionary of the English Language, while many American English spellings follow Websters An American Dictionary of the English Language. Webster was a proponent of English spelling reform for reasons both philological and nationalistic, in A Companion to the American Revolution, John Algeo notes, it is often assumed that characteristically American spellings were invented by Noah Webster. He was very influential in popularizing certain spellings in America, rather he chose already existing options such as center, color and check for the simplicity, analogy or etymology. William Shakespeares first folios, for example, used spellings like center and color as much as centre, Webster did attempt to introduce some reformed spellings, as did the Simplified Spelling Board in the early 20th century, but most were not adopted. In Britain, the influence of those who preferred the Norman spellings of words proved to be decisive, later spelling adjustments in the United Kingdom had little effect on todays American spellings and vice versa. For the most part, the systems of most Commonwealth countries. Australian spelling has also strayed slightly from British spelling, with some American spellings incorporated as standard, New Zealand spelling is almost identical to British spelling, except in the word fiord. There is also an increasing use of macrons in words that originated in Māori, most words ending in an unstressed -our in British English end in -or in American English. Wherever the vowel is unreduced in pronunciation, e. g. contour, velour, paramour and troubadour the spelling is the same everywhere, most words of this kind came from Latin, where the ending was spelled -or. They were first adopted into English from early Old French, after the Norman conquest of England, the ending became -our to match the Old French spelling. The -our ending was not only used in new English borrowings, however, -or was still sometimes found, and the first three folios of Shakespeares plays used both spellings before they were standardised to -our in the Fourth Folio of 1685. After the Renaissance, new borrowings from Latin were taken up with their original -or ending, Websters 1828 dictionary had only -or and is given much of the credit for the adoption of this form in the United States. Johnson, unlike Webster, was not an advocate of spelling reform and he preferred French over Latin spellings because, as he put it, the French generally supplied us. In Jeffersons original draft it is spelled honour, Honor and honour were equally frequent in Britain until the 17th century, honor still is, in the UK, the usual spelling as a persons name and appears in Honor Oak, a district of London. In derivatives and inflected forms of the words, British usage depends on the nature of the suffix used

2.
Transverse wave
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A transverse wave is a moving wave that consists of oscillations occurring perpendicular to the direction of energy transfer. If a transverse wave is moving in the positive x-direction, its oscillations are in up, light is an example of a transverse wave. With regard to transverse waves in matter, the displacement of the medium is perpendicular to the direction of propagation of the wave, a ripple in a pond and a wave on a string are easily visualized as transverse waves. Transverse waves are waves that are oscillating perpendicularly to the direction of propagation, if you anchor one end of a ribbon or string and hold the other end in your hand, you can create transverse waves by moving your hand up and down. Notice though, that you can also launch waves by moving your hand side-to-side, there are two independent directions in which wave motion can occur. In this case, these motions are the y and z directions mentioned above, continuing with the string example, if you carefully move your hand in a clockwise circle, you will launch waves in the form of a left-handed helix as they propagate away. Similarly, if you move your hand in a counter-clockwise circle and these phenomena of simultaneous motion in two directions go beyond the kinds of waves you can create on the surface of water, in general a wave on a string can be two-dimensional. Two-dimensional transverse waves exhibit a phenomenon called polarization, a wave produced by moving your hand in a line, up and down for instance, is a linearly polarized wave, a special case. A wave produced by moving your hand in a circle is a polarized wave. If your motion is not strictly in a line or a circle your hand will describe an ellipse, electromagnetic waves behave in this same way, although it is slightly harder to see. Electromagnetic waves are also two-dimensional transverse waves, ray theory does not describe phenomena such as interference and diffraction, which require wave theory. You can think of a ray of light, in optics, a light ray is a line or curve that is perpendicular to the lights wavefronts. Light rays bend at the interface between two media and may be curved in a medium in which the refractive index changes. Geometric optics describes how rays propagate through an optical system, the light wave diagram shows linear polarization. Each of these fields, the electric and the magnetic, exhibits two-dimensional transverse wave behavior, the transverse plane wave animation shown is also an example of linear polarization. The wave shown could occur on a water surface, transverse and Longitudinal Waves Introductory module on these waves at Connexions

3.
Wave
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In physics, a wave is an oscillation accompanied by a transfer of energy that travels through a medium. Frequency refers to the addition of time, wave motion transfers energy from one point to another, which displace particles of the transmission medium–that is, with little or no associated mass transport. Waves consist, instead, of oscillations or vibrations, around almost fixed locations, there are two main types of waves. Mechanical waves propagate through a medium, and the substance of this medium is deformed, restoring forces then reverse the deformation. For example, sound waves propagate via air molecules colliding with their neighbors, when the molecules collide, they also bounce away from each other. This keeps the molecules from continuing to travel in the direction of the wave, the second main type, electromagnetic waves, do not require a medium. Instead, they consist of periodic oscillations of electrical and magnetic fields generated by charged particles. These types vary in wavelength, and include radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, waves are described by a wave equation which sets out how the disturbance proceeds over time. The mathematical form of this varies depending on the type of wave. Further, the behavior of particles in quantum mechanics are described by waves, in addition, gravitational waves also travel through space, which are a result of a vibration or movement in gravitational fields. While mechanical waves can be transverse and longitudinal, all electromagnetic waves are transverse in free space. A single, all-encompassing definition for the wave is not straightforward. A vibration can be defined as a back-and-forth motion around a reference value, however, a vibration is not necessarily a wave. An attempt to define the necessary and sufficient characteristics that qualify a phenomenon as a results in a blurred line. The term wave is often understood as referring to a transport of spatial disturbances that are generally not accompanied by a motion of the medium occupying this space as a whole. In a wave, the energy of a vibration is moving away from the source in the form of a disturbance within the surrounding medium and it may appear that the description of waves is closely related to their physical origin for each specific instance of a wave process. For example, acoustics is distinguished from optics in that sound waves are related to a rather than an electromagnetic wave transfer caused by vibration. Concepts such as mass, momentum, inertia, or elasticity and this difference in origin introduces certain wave characteristics particular to the properties of the medium involved

4.
Oscillation
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Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. The term vibration is used to describe mechanical oscillation. Familiar examples of oscillation include a swinging pendulum and alternating current power, the simplest mechanical oscillating system is a weight attached to a linear spring subject to only weight and tension. Such a system may be approximated on an air table or ice surface, the system is in an equilibrium state when the spring is static. If the system is displaced from the equilibrium, there is a net restoring force on the mass, tending to bring it back to equilibrium. However, in moving the back to the equilibrium position, it has acquired momentum which keeps it moving beyond that position. If a constant force such as gravity is added to the system, the time taken for an oscillation to occur is often referred to as the oscillatory period. All real-world oscillator systems are thermodynamically irreversible and this means there are dissipative processes such as friction or electrical resistance which continually convert some of the energy stored in the oscillator into heat in the environment. Thus, oscillations tend to decay with time there is some net source of energy into the system. The simplest description of this process can be illustrated by oscillation decay of the harmonic oscillator. In addition, a system may be subject to some external force. In this case the oscillation is said to be driven, some systems can be excited by energy transfer from the environment. This transfer typically occurs where systems are embedded in some fluid flow, at sufficiently large displacements, the stiffness of the wing dominates to provide the restoring force that enables an oscillation. The harmonic oscillator and the systems it models have a degree of freedom. More complicated systems have more degrees of freedom, for two masses and three springs. In such cases, the behavior of each variable influences that of the others and this leads to a coupling of the oscillations of the individual degrees of freedom. For example, two pendulum clocks mounted on a wall will tend to synchronise. This phenomenon was first observed by Christiaan Huygens in 1665, more special cases are the coupled oscillators where energy alternates between two forms of oscillation

5.
String (music)
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A string is the vibrating element that produces sound in string instruments such as the guitar, harp, piano, and members of the violin family. Strings are lengths of a material that a musical instrument holds under tension so that they can vibrate freely. Wound strings have a core of one material, with an overwinding of other materials and this is to make the string vibrate at the desired pitch, while maintaining a low profile and sufficient flexibility for playability. This enabled stringed instruments to be made with less thick bass strings, on string instruments that the player plucks or bows directly, this enabled instrument makers to use thinner strings for the lowest-pitched strings, which made the lower-pitch strings easier to play. The end of the string that mounts to the tuning mechanism is usually plain. Depending on the instrument, the other, fixed end may have either a plain, loop. When a ball or loop is used with a guitar, this ensures that the string stays fixed in the bridge of the guitar, when a ball or loop is used with a violin-family instrument, this keeps the string end fixed in the tailpiece. Fender Bullet strings have a cylinder for more stable tuning on guitars equipped with synchronized tremolo systems. Strings for some instruments may be wrapped with silk at the ends to protect the string, the color and pattern of the silk often identifies attributes of the string, such as manufacturer, size, intended pitch, etc. There are several varieties of wound strings available, the simplest wound strings are roundwound—with round wire wrapped in a tight spiral around either a round or hexagonal core. Such strings are usually simple to manufacture and the least expensive and they have several drawbacks, however, Roundwound strings have a bumpy surface profile that produce friction on the players fingertips. This causes squeaking sounds when the fingers slide over the strings. Roundwound strings higher friction surface profile may hasten fingerboard and fret wear, when the core is round, the winding is less secure and may rotate freely around the core, especially if the winding is damaged after use. Flatwound strings also have either a round or hex core, however, the winding wire has a rounded square cross-section that has a shallower profile when tightly wound. This makes for more playing, and decreased wear for frets. Squeaking sounds due to fingers sliding along the strings are also decreased significantly, flatwound strings also have a longer playable life because of smaller grooves for dirt and oil to build up in. On the other hand, flatwound strings sound less bright than roundwounds, flatwounds also usually cost more than roundwounds because of less demand, less production, and higher overhead costs. Manufacturing is also difficult, as precise alignment of the flat sides of the winding must be maintained

6.
Sound
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In physics, sound is a vibration that propagates as a typically audible mechanical wave of pressure and displacement, through a transmission medium such as air or water. In physiology and psychology, sound is the reception of such waves, humans can hear sound waves with frequencies between about 20 Hz and 20 kHz. Sound above 20 kHz is ultrasound and below 20 Hz is infrasound, other animals have different hearing ranges. Acoustics is the science that deals with the study of mechanical waves in gases, liquids, and solids including vibration, sound, ultrasound. A scientist who works in the field of acoustics is an acoustician, an audio engineer, on the other hand, is concerned with the recording, manipulation, mixing, and reproduction of sound. Auditory sensation evoked by the oscillation described in, sound can propagate through a medium such as air, water and solids as longitudinal waves and also as a transverse wave in solids. The sound waves are generated by a source, such as the vibrating diaphragm of a stereo speaker. The sound source creates vibrations in the surrounding medium, as the source continues to vibrate the medium, the vibrations propagate away from the source at the speed of sound, thus forming the sound wave. At a fixed distance from the source, the pressure, velocity, at an instant in time, the pressure, velocity, and displacement vary in space. Note that the particles of the medium do not travel with the sound wave and this is intuitively obvious for a solid, and the same is true for liquids and gases. During propagation, waves can be reflected, refracted, or attenuated by the medium, the behavior of sound propagation is generally affected by three things, A complex relationship between the density and pressure of the medium. This relationship, affected by temperature, determines the speed of sound within the medium, if the medium is moving, this movement may increase or decrease the absolute speed of the sound wave depending on the direction of the movement. For example, sound moving through wind will have its speed of propagation increased by the speed of the if the sound and wind are moving in the same direction. If the sound and wind are moving in opposite directions, the speed of the wave will be decreased by the speed of the wind. Medium viscosity determines the rate at which sound is attenuated, for many media, such as air or water, attenuation due to viscosity is negligible. When sound is moving through a medium that does not have constant physical properties, the mechanical vibrations that can be interpreted as sound can travel through all forms of matter, gases, liquids, solids, and plasmas. The matter that supports the sound is called the medium, sound cannot travel through a vacuum. Sound is transmitted through gases, plasma, and liquids as longitudinal waves and it requires a medium to propagate

7.
Electromagnetic radiation
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In physics, electromagnetic radiation refers to the waves of the electromagnetic field, propagating through space carrying electromagnetic radiant energy. It includes radio waves, microwaves, infrared, light, ultraviolet, X-, classically, electromagnetic radiation consists of electromagnetic waves, which are synchronized oscillations of electric and magnetic fields that propagate at the speed of light through a vacuum. The oscillations of the two fields are perpendicular to other and perpendicular to the direction of energy and wave propagation. The wavefront of electromagnetic waves emitted from a point source is a sphere, the position of an electromagnetic wave within the electromagnetic spectrum can be characterized by either its frequency of oscillation or its wavelength. Electromagnetic waves are produced whenever charged particles are accelerated, and these waves can interact with other charged particles. EM waves carry energy, momentum and angular momentum away from their source particle, quanta of EM waves are called photons, whose rest mass is zero, but whose energy, or equivalent total mass, is not zero so they are still affected by gravity. Thus, EMR is sometimes referred to as the far field, in this language, the near field refers to EM fields near the charges and current that directly produced them, specifically, electromagnetic induction and electrostatic induction phenomena. In the quantum theory of electromagnetism, EMR consists of photons, quantum effects provide additional sources of EMR, such as the transition of electrons to lower energy levels in an atom and black-body radiation. The energy of a photon is quantized and is greater for photons of higher frequency. This relationship is given by Plancks equation E = hν, where E is the energy per photon, ν is the frequency of the photon, a single gamma ray photon, for example, might carry ~100,000 times the energy of a single photon of visible light. The effects of EMR upon chemical compounds and biological organisms depend both upon the power and its frequency. EMR of visible or lower frequencies is called non-ionizing radiation, because its photons do not individually have enough energy to ionize atoms or molecules, the effects of these radiations on chemical systems and living tissue are caused primarily by heating effects from the combined energy transfer of many photons. In contrast, high ultraviolet, X-rays and gamma rays are called ionizing radiation since individual photons of high frequency have enough energy to ionize molecules or break chemical bonds. These radiations have the ability to cause chemical reactions and damage living cells beyond that resulting from simple heating, Maxwell derived a wave form of the electric and magnetic equations, thus uncovering the wave-like nature of electric and magnetic fields and their symmetry. Because the speed of EM waves predicted by the wave equation coincided with the speed of light. Maxwell’s equations were confirmed by Heinrich Hertz through experiments with radio waves, according to Maxwells equations, a spatially varying electric field is always associated with a magnetic field that changes over time. Likewise, a varying magnetic field is associated with specific changes over time in the electric field. In an electromagnetic wave, the changes in the field are always accompanied by a wave in the magnetic field in one direction

8.
Light
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Light is electromagnetic radiation within a certain portion of the electromagnetic spectrum. The word usually refers to light, which is visible to the human eye and is responsible for the sense of sight. Visible light is defined as having wavelengths in the range of 400–700 nanometres, or 4.00 × 10−7 to 7.00 × 10−7 m. This wavelength means a range of roughly 430–750 terahertz. The main source of light on Earth is the Sun, sunlight provides the energy that green plants use to create sugars mostly in the form of starches, which release energy into the living things that digest them. This process of photosynthesis provides virtually all the used by living things. Historically, another important source of light for humans has been fire, with the development of electric lights and power systems, electric lighting has effectively replaced firelight. Some species of animals generate their own light, a process called bioluminescence, for example, fireflies use light to locate mates, and vampire squids use it to hide themselves from prey. Visible light, as all types of electromagnetic radiation, is experimentally found to always move at this speed in a vacuum. In physics, the term sometimes refers to electromagnetic radiation of any wavelength. In this sense, gamma rays, X-rays, microwaves and radio waves are also light, like all types of light, visible light is emitted and absorbed in tiny packets called photons and exhibits properties of both waves and particles. This property is referred to as the wave–particle duality, the study of light, known as optics, is an important research area in modern physics. Generally, EM radiation, or EMR, is classified by wavelength into radio, microwave, infrared, the behavior of EMR depends on its wavelength. Higher frequencies have shorter wavelengths, and lower frequencies have longer wavelengths, when EMR interacts with single atoms and molecules, its behavior depends on the amount of energy per quantum it carries. There exist animals that are sensitive to various types of infrared, infrared sensing in snakes depends on a kind of natural thermal imaging, in which tiny packets of cellular water are raised in temperature by the infrared radiation. EMR in this range causes molecular vibration and heating effects, which is how these animals detect it, above the range of visible light, ultraviolet light becomes invisible to humans, mostly because it is absorbed by the cornea below 360 nanometers and the internal lens below 400. Furthermore, the rods and cones located in the retina of the eye cannot detect the very short ultraviolet wavelengths and are in fact damaged by ultraviolet. Many animals with eyes that do not require lenses are able to detect ultraviolet, by quantum photon-absorption mechanisms, various sources define visible light as narrowly as 420 to 680 to as broadly as 380 to 800 nm

9.
Radio wave
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Radio waves are a type of electromagnetic radiation with wavelengths in the electromagnetic spectrum longer than infrared light. Radio waves have frequencies as high as 300 GHz to as low as 3 kHz, though some definitions describe waves above 1 or 3 GHz as microwaves, at 300 GHz, the corresponding wavelength is 1 mm, and at 3 kHz is 100 km. Like all other electromagnetic waves, they travel at the speed of light, naturally occurring radio waves are generated by lightning, or by astronomical objects. Radio waves are generated by radio transmitters and received by radio receivers, the radio spectrum is divided into a number of radio bands on the basis of frequency, allocated to different uses. Radio waves were first predicted by mathematical work done in 1867 by Scottish mathematical physicist James Clerk Maxwell, Maxwell noticed wavelike properties of light and similarities in electrical and magnetic observations. Radio waves were first used for communication in the mid 1890s by Guglielmo Marconi, different frequencies experience different combinations of these phenomena in the Earths atmosphere, making certain radio bands more useful for specific purposes than others. It does not necessarily require a cleared sight path, at lower frequencies radio waves can pass through buildings, foliage and this is the only method of propagation possible at microwave frequencies and above. On the surface of the Earth, line of propagation is limited by the visual horizon to about 40 miles. This is the used by cell phones, cordless phones, walkie-talkies, wireless networks, FM and television broadcasting. Indirect propagation, Radio waves can reach points beyond the line-of-sight by diffraction, diffraction allows a radio wave to bend around obstructions such as a building edge, a vehicle, or a turn in a hall. Radio waves also reflect from surfaces such as walls, floors, ceilings, vehicles and these effects are used in short range radio communication systems. Ground waves allow mediumwave and longwave broadcasting stations to have coverage areas beyond the horizon, the nonzero resistance of the earth absorbs energy from ground waves, so as they propagate the waves lose power and the wavefronts bend over at an angle to the surface. As frequency decreases, the decrease and the achievable range increases. Military very low frequency and extremely low frequency communication systems can communicate over most of the Earth, and with submarines hundreds of feet underwater. Tropospheric propagation, In the VHF and UHF bands, radio waves can travel somewhat beyond the horizon due to refraction in the troposphere. This is due to changes in the index of air with temperature and pressure. At times, radio waves can travel up to 500 -1000 km due to tropospheric ducting and these effects are variable and not as reliable as ionospheric propagation, below. So radio waves directed at an angle into the sky can return to Earth beyond the horizon, by using multiple skips communication at intercontinental distances can be achieved

10.
Gravitational wave
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Gravitational waves are ripples in the curvature of spacetime that propagate as waves at the speed of light, generated in certain gravitational interactions that propagate outward from their source. The possibility of gravitational waves was discussed in 1893 by Oliver Heaviside using the analogy between the law in gravitation and electricity. In 1905 Henri Poincaré first proposed gravitational waves emanating from a body, Gravitational waves cannot exist in the Newtons law of universal gravitation, since that law is predicated on the assumption that physical interactions propagate at infinite speed. On June 15,2016, a detection of gravitational waves from coalescing black holes was announced. Besides LIGO, many other observatories are under construction. In Einsteins theory of relativity, gravity is treated as a phenomenon resulting from the curvature of spacetime. This curvature is caused by the presence of mass, generally, the more mass that is contained within a given volume of space, the greater the curvature of spacetime will be at the boundary of its volume. As objects with mass move around in spacetime, the changes to reflect the changed locations of those objects. In certain circumstances, accelerating objects generate changes in this curvature and these propagating phenomena are known as gravitational waves. As a gravitational wave passes an observer, that observer will find spacetime distorted by the effects of strain, distances between objects increase and decrease rhythmically as the wave passes, at a frequency corresponding to that of the wave. This occurs despite such free objects never being subjected to an unbalanced force, the magnitude of this effect decreases proportional to the inverse distance from the source. Inspiraling binary neutron stars are predicted to be a source of gravitational waves as they coalesce. However, due to the distances to these sources, the effects when measured on Earth are predicted to be very small. Scientists have demonstrated the existence of these waves with ever more sensitive detectors, the most sensitive detector accomplished the task possessing a sensitivity measurement of about one part in 5×1022 provided by the LIGO and VIRGO observatories. A space based observatory, the Laser Interferometer Space Antenna, is currently under development by ESA, Gravitational waves can penetrate regions of space that electromagnetic waves cannot. They are able to allow the observation of the merger of black holes, such systems cannot be observed with more traditional means such as optical telescopes or radio telescopes, and so gravitational-wave astronomy gives new insights into the working of the Universe. In particular, gravitational waves could be of interest to cosmologists as they offer a way of observing the very early Universe. This is not possible with conventional astronomy, since before recombination the Universe was opaque to electromagnetic radiation, precise measurements of gravitational waves will also allow scientists to test more thoroughly the general theory of relativity

11.
S-wave
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The S-wave moves as a shear or transverse wave, so motion is perpendicular to the direction of wave propagation. The wave moves through elastic media, and the restoring force comes from shear effects. Unlike the P-wave, the S-wave cannot travel through the outer core of the Earth. They can still appear in the inner core, when a P-wave strikes the boundary of molten. And when the S-waves hit the boundary again they will in turn create P-waves and this property allows seismologists to determine the nature of the inner core. As transverse waves, S-waves exhibit properties, such as polarization and birefringence, S-waves polarized in the horizontal plane are classified as SH-waves. If polarized in the plane, they are classified as SV-waves. When an S- or P-wave strikes an interface at an other than 90 degrees. As described above, if the interface is between a solid and liquid, S becomes P or vice versa, however, even if the interface is between two solid media, mode conversion results. If a P-wave strikes an interface, four propagation modes may result, reflected and transmitted P, similarly, if an SV-wave strikes an interface, the same four modes occur in different proportions. The exact amplitudes of all waves are described by the Zoeppritz equations. The prediction of S-waves came out of theory in the 1800s, taking the divergence of seismic wave equation in homogeneous media, instead of the curl, yields an equation describing P-wave propagation. The steady-state SH waves are defined by the Helmholtz equation u =0 where k is the wave number, earthquake Early Warning Lamb waves Longitudinal wave Love wave P-wave Rayleigh wave Seismic wave Shear wave splitting Surface wave Shearer, Peter. Aki, Keiiti, Richards, Paul G. Quantitative Seismology

12.
Gravity wave
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In fluid dynamics, gravity waves are waves generated in a fluid medium or at the interface between two media when the force of gravity or buoyancy tries to restore equilibrium. An example of such an interface is that between the atmosphere and the ocean, which rise to wind waves. A gravity wave results when fluid is displaced from a position of equilibrium, the restoration of the fluid to equilibrium will produce a movement of the fluid back and forth, called a wave orbit. Gravity waves on an interface of the ocean are called surface gravity waves or surface waves. Wind-generated waves on the surface are examples of gravity waves, as are tsunamis. Wind-generated gravity waves on the surface of the Earths ponds, lakes, seas. Shorter waves are affected by surface tension and are called gravity–capillary waves. Alternatively, so-called infragravity waves, which are due to nonlinear wave interaction with the wind waves, have periods longer than the accompanying wind-generated waves. In the Earths atmosphere, gravity waves are a mechanism that produce the transfer of momentum from the troposphere to the stratosphere and mesosphere, Gravity waves are generated in the troposphere by frontal systems or by airflow over mountains. At first, waves propagate through the atmosphere without appreciable change in mean velocity, but as the waves reach more rarefied air at higher altitudes, their amplitude increases, and nonlinear effects cause the waves to break, transferring their momentum to the mean flow. This transfer of momentum is responsible for the forcing of the many large-scale dynamical features of the atmosphere, thus, this process plays a key role in the dynamics of the middle atmosphere. The effect of gravity waves in clouds can look like altostratus undulatus clouds, and are confused with them. The phase velocity c of a gravity wave with wavenumber k is given by the formula c = g k. When surface tension is important, this is modified to c = g k + σ k ρ, where σ is the surface tension coefficient and ρ is the density. Since c = ω / k is the speed in terms of the angular frequency ω and the wavenumber. The group velocity of a wave is given by c g = d ω d k, the group velocity is one half the phase velocity. A wave in which the group and phase velocities differ is called dispersive, Gravity waves traveling in shallow water, are nondispersive, the phase and group velocities are identical and independent of wavelength and frequency. When the water depth is h, c p = c g = g h, wind waves, as their name suggests, are generated by wind transferring energy from the atmosphere to the oceans surface, and capillary-gravity waves play an essential role in this effect

13.
Electric field
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An electric field is a vector field that associates to each point in space the Coulomb force that would be experienced per unit of electric charge, by an infinitesimal test charge at that point. Electric fields are created by electric charges and can be induced by time-varying magnetic fields, the electric field combines with the magnetic field to form the electromagnetic field. The electric field, E, at a point is defined as the force, F. A particle of charge q would be subject to a force F = q E and its SI units are newtons per coulomb or, equivalently, volts per metre, which in terms of SI base units are kg⋅m⋅s−3⋅A−1. Electric fields are caused by electric charges or varying magnetic fields, in the special case of a steady state, the Maxwell-Faraday inductive effect disappears. The resulting two equations, taken together, are equivalent to Coulombs law, written as E =14 π ε0 ∫ d r ′ ρ r − r ′ | r − r ′ |3 for a charge density ρ. Notice that ε0, the permittivity of vacuum, must be substituted if charges are considered in non-empty media, the equations of electromagnetism are best described in a continuous description. A charge q located at r 0 can be described mathematically as a charge density ρ = q δ, conversely, a charge distribution can be approximated by many small point charges. Electric fields satisfy the principle, because Maxwells equations are linear. This principle is useful to calculate the field created by point charges. Q n are stationary in space at r 1, r 2, in that case, Coulombs law fully describes the field. If a system is static, such that magnetic fields are not time-varying, then by Faradays law, in this case, one can define an electric potential, that is, a function Φ such that E = − ∇ Φ. This is analogous to the gravitational potential, Coulombs law, which describes the interaction of electric charges, F = q = q E is similar to Newtons law of universal gravitation, F = m = m g. This suggests similarities between the electric field E and the gravitational field g, or their associated potentials, mass is sometimes called gravitational charge because of that similarity. Electrostatic and gravitational forces both are central, conservative and obey an inverse-square law, a uniform field is one in which the electric field is constant at every point. It can be approximated by placing two conducting plates parallel to other and maintaining a voltage between them, it is only an approximation because of boundary effects. Assuming infinite planes, the magnitude of the electric field E is, electrodynamic fields are E-fields which do change with time, for instance when charges are in motion. The electric field cannot be described independently of the field in that case

14.
Magnetic field
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A magnetic field is the magnetic effect of electric currents and magnetic materials. The magnetic field at any point is specified by both a direction and a magnitude, as such it is represented by a vector field. The term is used for two distinct but closely related fields denoted by the symbols B and H, where H is measured in units of amperes per meter in the SI, B is measured in teslas and newtons per meter per ampere in the SI. B is most commonly defined in terms of the Lorentz force it exerts on moving electric charges, Magnetic fields can be produced by moving electric charges and the intrinsic magnetic moments of elementary particles associated with a fundamental quantum property, their spin. In quantum physics, the field is quantized and electromagnetic interactions result from the exchange of photons. Magnetic fields are used throughout modern technology, particularly in electrical engineering. The Earth produces its own field, which is important in navigation. Rotating magnetic fields are used in electric motors and generators. Magnetic forces give information about the carriers in a material through the Hall effect. The interaction of magnetic fields in electric devices such as transformers is studied in the discipline of magnetic circuits, noting that the resulting field lines crossed at two points he named those points poles in analogy to Earths poles. He also clearly articulated the principle that magnets always have both a north and south pole, no matter how finely one slices them, almost three centuries later, William Gilbert of Colchester replicated Petrus Peregrinus work and was the first to state explicitly that Earth is a magnet. Published in 1600, Gilberts work, De Magnete, helped to establish magnetism as a science, in 1750, John Michell stated that magnetic poles attract and repel in accordance with an inverse square law. Charles-Augustin de Coulomb experimentally verified this in 1785 and stated explicitly that the north and south poles cannot be separated, building on this force between poles, Siméon Denis Poisson created the first successful model of the magnetic field, which he presented in 1824. In this model, a magnetic H-field is produced by magnetic poles, three discoveries challenged this foundation of magnetism, though. First, in 1819, Hans Christian Ørsted discovered that an electric current generates a magnetic field encircling it, then in 1820, André-Marie Ampère showed that parallel wires having currents in the same direction attract one another. Finally, Jean-Baptiste Biot and Félix Savart discovered the Biot–Savart law in 1820, extending these experiments, Ampère published his own successful model of magnetism in 1825. This has the benefit of explaining why magnetic charge can not be isolated. Also in this work, Ampère introduced the term electrodynamics to describe the relationship between electricity and magnetism, in 1831, Michael Faraday discovered electromagnetic induction when he found that a changing magnetic field generates an encircling electric field

15.
Linear polarization
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The orientation of a linearly polarized electromagnetic wave is defined by the direction of the electric field vector. For example, if the field vector is vertical the radiation is said to be vertically polarized. Here ∣ E ∣ is the amplitude of the field and | ψ ⟩ = d e f = is the Jones vector in the x-y plane. The wave is polarized when the phase angles α x, α y are equal. This represents a wave polarized at an angle θ with respect to the x axis, in that case, the Jones vector can be written | ψ ⟩ = exp ⁡. The state vectors for linear polarization in x or y are special cases of this state vector, sinusoidal plane-wave solutions of the electromagnetic wave equation Polarization Circular polarization Elliptical polarization Photon polarization Jackson, John D

16.
Circular polarization
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In electrodynamics the strength and direction of an electric field is defined by its electric field vector. In the case of a polarized wave, as seen in the accompanying animation. At any instant of time, the field vector of the wave describes a helix along the direction of propagation. Circular polarization is a case of the more general condition of elliptical polarization. The other special case is the linear polarization. The phenomenon of polarization arises as a consequence of the fact that light behaves as a transverse wave. On the right is an illustration of the electric field vectors of a circularly polarized electromagnetic wave, the electric field vectors have a constant magnitude but their direction changes in a rotary manner. Given that this is a wave, each vector represents the magnitude. Specifically, given that this is a circularly polarized plane wave, refer to these two images in the plane wave article to better appreciate this. This light is considered to be right-hand, clockwise circularly polarized if viewed by the receiver, as a result, the magnetic field vectors would trace out a second helix if displayed. Circular polarization is often encountered in the field of optics and in this section, refer to the second illustration on the right. The vertical component and its plane are illustrated in blue while the horizontal component. Notice that the horizontal component leads the vertical component by one quarter of a wavelength. The result of this alignment is that there are select vectors, corresponding to the helix, to appreciate how this quadrature phase shift corresponds to an electric field that rotates while maintaining a constant magnitude, imagine a dot traveling clockwise in a circle. Consider how the vertical and horizontal displacements of the dot, relative to the center of the circle, now referring again to the illustration, imagine the center of the circle just described, traveling along the axis from the front to the back. The circling dot will trace out a helix with the displacement toward our viewing left, the next pair of illustrations is that of left-handed, counter-clockwise circularly polarized light when viewed by the receiver. Because it is left-handed, the horizontal component is now lagging the vertical component by one quarter of a wavelength rather than leading it. To convert a given handedness of polarized light to the other one can use a half-wave plate

17.
Elliptical polarization
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An elliptically polarized wave may be resolved into two linearly polarized waves in phase quadrature, with their polarization planes at right angles to each other. Since the electric field can rotate clockwise or counterclockwise as it propagates, other forms of polarization, such as circular and linear polarization, can be considered to be special cases of elliptical polarization. Here ∣ E ∣ is the amplitude of the field and | ψ ⟩ = d e f = is the normalized Jones vector and this is the most complete representation of polarized electromagnetic radiation and corresponds in general to elliptical polarization. At a fixed point in space, the electric vector E traces out an ellipse in the x-y plane, the orientation of the ellipse is given by the angle ϕ the semi-major axis makes with the x-axis. This angle can be calculated from tan ⁡2 ϕ = tan ⁡2 θ cos ⁡ β, if β =0, the wave is linearly polarized. The ellipse collapses to a straight line ( A = | E |, B =0 {\displaystyle oriented at an angle ϕ = θ. This is the case of superposition of two simple motions, one in the x direction with an amplitude | E | cos ⁡ θ. If β = ± π /2 and θ = π /4, A = B = | E | /2, i. e. the wave is circularly polarized. When β = π /2, the wave is polarized, and when β = − π /2. Animation of Elliptical Polarization Comparison of Elliptical Polarization with Linear and Circular Polarizations

18.
Right-hand rule
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In mathematics and physics, the right-hand rule is a common mnemonic for understanding orientation conventions for vectors in three dimensions. Most of the left and right-hand rules arise from the fact that the three axes of 3-dimensional space have two possible orientations. This can be seen by holding your hands outward and together, palms up, with the fingers curled. If the curl of your fingers represents a movement from the first or X axis to the second or Y axis then the third or Z axis can point either along your left thumb or right thumb. Left and right-hand rules arise when dealing with co-ordinate axes, rotation, spirals, electromagnetic fields, mirror images and enantiomers in mathematics and chemistry. For right-handed coordinates your right thumb points along the Z axis in a positive Z-direction, when viewed from the top or Z axis the system is counter-clockwise. When viewed from the top or Z axis the system is clockwise, interchanging the labels of any two axes reverses the handedness. Reversing the direction of one axis also reverses the handedness, reversing two axes amounts to a 180° rotation around the remaining axis. In mathematics a rotating body is represented by a vector along the axis of rotation. This allows some easy calculations using the cross product. Note that no part of the body is moving in the direction of the axis arrow, by coincidence, if your thumb points north the earth rotates according to the right-hand rule. This causes the sun and stars to appear to revolve according to the left-hand rule, a helix, to use a more accurate term than spiral, is basically a circular curve that advances along the z-axis while rotating in the x-y plane. Helices are either right- or left-handed, curled fingers giving the direction of rotation, the two types are mirror images of each other, physically distinct and cannot be transformed into each other by any physical operation such as turning them over. The threads on a right-handed screw are a right-handed helix and they are basically a long inclined plane wrapped around a cylinder such that turning the screw advances the screw back and forth along the z-axis. From the point of view of the threads, turning the screw forces the screw up or down the inclined plane. If a screw is right-handed the rule is this, point your right thumb in the direction you want the screw to go and turn the screw in the direction of your curled right fingers. Viewed from the earth, the path of an object moving in a straight line appears to bend to the right in the northern hemisphere. This causes low-pressure areas in the northern hemispheres to rotate according to the right-hand rule, handedness is not obvious here but it is clear in the underlying mathematics

19.
Incandescent light bulb
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An incandescent light bulb, incandescent lamp or incandescent light globe is an electric light with a wire filament heated to such a high temperature that it glows with visible light. The filament, heated by passing a current through it, is protected from oxidation with a glass or quartz bulb that is filled with inert gas or evacuated. In a halogen lamp, filament evaporation is prevented by a process that redeposits metal vapor onto the filament. The light bulb is supplied with current by feed-through terminals or wires embedded in the glass. Most bulbs are used in a socket which provides mechanical support, Incandescent bulbs are manufactured in a wide range of sizes, light output, and voltage ratings, from 1.5 volts to about 300 volts. They require no external regulating equipment, have low manufacturing costs, the remaining energy is converted into heat. The luminous efficacy of an incandescent bulb is 16 lumens per watt. Some applications of the incandescent bulb deliberately use the heat generated by the filament, such applications include incubators, brooding boxes for poultry, heat lights for reptile tanks, infrared heating for industrial heating and drying processes, lava lamps, and the Easy-Bake Oven toy. In addressing the question of who invented the incandescent lamp, historians Robert Friedel and Paul Israel list 22 inventors of incandescent lamps prior to Joseph Swan, historian Thomas Hughes has attributed Edisons success to his development of an entire, integrated system of electric lighting. In 1761 Ebenezer Kinnersley demonstrated heating a wire to incandescence and it was not bright enough nor did it last long enough to be practical, but it was the precedent behind the efforts of scores of experimenters over the next 75 years. Over the first three-quarters of the 19th century many experimenters worked with various combinations of platinum or iridium wires, carbon rods, many of these devices were demonstrated and some were patented. In 1835, James Bowman Lindsay demonstrated a constant electric light at a meeting in Dundee. He stated that he could read a book at a distance of one, however, having perfected the device to his own satisfaction, he turned to the problem of wireless telegraphy and did not develop the electric light any further. His claims are not well documented, although he is credited in Challoner et al. with being the inventor of the Incandescent Light Bulb, in 1838, Belgian lithographer Marcellin Jobard invented an incandescent light bulb with a vacuum atmosphere using a carbon filament. In 1840, British scientist Warren de la Rue enclosed a coiled platinum filament in a vacuum tube, although a workable design, the cost of the platinum made it impractical for commercial use. In 1841, Frederick de Moleyns of England was granted the first patent for an incandescent lamp, in 1845, American John W. Starr acquired a patent for his incandescent light bulb involving the use of carbon filaments. He died shortly after obtaining the patent, and his invention was never produced commercially, little else is known about him. In 1851, Jean Eugène Robert-Houdin publicly demonstrated incandescent light bulbs on his estate in Blois and his light bulbs are on display in the museum of the Château de Blois

20.
Polarizer
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A polarizer or polariser is an optical filter that lets light waves of a specific polarization pass and blocks light waves of other polarizations. It can convert a beam of light of undefined or mixed polarization into a beam of well-defined polarization, the common types of polarizers are linear polarizers and circular polarizers. Polarizers are used in many techniques and instruments, and polarizing filters find applications in photography. Polarizers can also be made for other types of electromagnetic waves besides light, such as waves, microwaves. The simplest linear polarizer is the wire-grid polarizer, which consists of many fine parallel wires that are placed in a plane perpendicular to the incident beam. Electromagnetic waves which have a component of their electric fields aligned parallel to the wires will induce the movement of electrons along the length of the wires, for waves with electric fields perpendicular to the wires, the electrons cannot move very far across the width of each wire. Therefore, little energy is reflected and the incident wave is able to pass through the grid, in this case the grid behaves like a dielectric material. Overall, this causes the wave to be linearly polarized with an electric field that is completely perpendicular to the wires. The hypothesis that the waves slip through the gaps between the wires is incorrect, for practical purposes, the separation between wires must be less than the wavelength of the incident radiation. In addition, the width of each wires should be compared to the spacing between wires. Therefore, it is easy to construct wire-grid polarizers for microwaves, far-infrared. In addition, advanced techniques can also build very tight pitch metallic grids. Since the degree of polarization depends little on wavelength and angle of incidence, certain crystals, due to the effects described by crystal optics, show dichroism, preferential absorption of light which is polarized in particular directions. They can therefore be used as linear polarizers, the best known crystal of this type is tourmaline. However, this crystal is used as a polarizer, since the dichroic effect is strongly wavelength dependent. Herapathite is also dichroic, and is not strongly coloured, but is difficult to grow in large crystals, a Polaroid polarizing filter functions similarly on an atomic scale to the wire-grid polarizer. It was originally made of microscopic herapathite crystals and its current H-sheet form is made from polyvinyl alcohol plastic with an iodine doping. Stretching of the sheet during manufacture causes the PVA chains to align in one particular direction, valence electrons from the iodine dopant are able to move linearly along the polymer chains, but not transverse to them

21.
Isotropy
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Isotropy is uniformity in all orientations, it is derived from the Greek isos and tropos. Precise definitions depend on the subject area, exceptions, or inequalities, are frequently indicated by the prefix an, hence anisotropy. Anisotropy is also used to describe situations where properties vary systematically, Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented. Within mathematics, isotropy has a few different meanings, Isotropic manifolds A manifold is isotropic if the geometry on the manifold is the same regardless of direction, a manifold can be homogeneous without being isotropic, but if it is inhomogeneous, it is necessarily anisotropic. Isotropic quadratic form A quadratic form q is said to be if there is a non-zero vector v such that q =0. In complex geometry, a line through the origin in the direction of a vector is an isotropic line. Isotropic coordinates Isotropic coordinates are coordinates on a chart for Lorentzian manifolds. Isotropy group An isotropy group is the group of isomorphisms from any object to itself in a groupoid, Isotropic position A probability distribution over a vector space is in isotropic position if its covariance matrix is the identity. This follows from invariance of the Hamiltonian, which in turn is guaranteed for a spherically symmetric potential. Kinetic theory of gases is also an example of isotropy and it is assumed that the molecules move in random directions and as a consequence, there is an equal probability of a molecule moving in any direction. Thus when there are molecules in the gas, with high probability there will be very similar numbers moving in one direction as any other hence demonstrating approximate isotropy. Fluid dynamics Fluid flow is isotropic if there is no directional preference, an example of anisotropy is in flows with a background density as gravity works in only one direction. The apparent surface separating two differing isotropic fluids would be referred to as an isotrope, thermal expansion A solid is said to be isotropic if the expansion of solid is equal in all directions when thermal energy is provided to the solid. Electromagnetics An isotropic medium is one such that the permittivity, ε, and permeability, μ, of the medium are uniform in all directions of the medium, optics Optical isotropy means having the same optical properties in all directions. The individual reflectance or transmittance of the domains is averaged if the macroscopic reflectance or transmittance is to be calculated, cosmology The Big Bang theory of the evolution of the observable universe assumes that space is isotropic. It also assumes that space is homogeneous and these two assumptions together are known as the Cosmological Principle. As of 2006, the observations suggest that, on scales much larger than galaxies, galaxy clusters are Great features. Here homogeneous means that the universe is the same everywhere and isotropic implies that there is no preferred direction, in the study of mechanical properties of materials, isotropic means having identical values of a property in all directions

22.
Birefringence
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Birefringence is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light. These optically anisotropic materials are said to be birefringent, the birefringence is often quantified as the maximum difference between refractive indices exhibited by the material. Crystals with non-cubic crystal structures are often birefringent, as are plastics under mechanical stress and this effect was first described by the Danish scientist Rasmus Bartholin in 1669, who observed it in calcite, a crystal having one of the strongest birefringences. A mathematical description of wave propagation in a birefringent medium is presented below, following is a qualitative explanation of the phenomenon. Thus rotating the material around this axis does not change its optical behavior and this special direction is known as the optic axis of the material. Light whose polarization is perpendicular to the axis is governed by a refractive index no. Light whose polarization is in the direction of the optic axis sees an optical index ne, for any ray direction there is a linear polarization direction perpendicular to the optic axis, and this is called an ordinary ray. The magnitude of the difference is quantified by the birefringence, Δ n = n e − n o, the propagation of the ordinary ray is simply described by no as if there were no birefringence involved. However the extraordinary ray, as its name suggests, propagates unlike any wave in an optical material. Its refraction at a surface can be using the effective refractive index. However it is in fact an inhomogeneous wave whose power flow is not exactly in the direction of the wave vector and this causes an additional shift in that beam, even when launched at normal incidence, as is popularly observed using a crystal of calcite as photographed above. Rotating the calcite crystal will cause one of the two images, that of the ray, to rotate slightly around that of the ordinary ray. When the light propagates either along or orthogonal to the optic axis, in the first case, both polarizations see the same effective refractive index, so there is no extraordinary ray. In the second case the extraordinary ray propagates at a different phase velocity but is not an inhomogeneous wave, for instance, a quarter-wave plate is commonly used to create circular polarization from a linearly polarized source. The case of so-called biaxial crystals is substantially more complex and these are characterized by three refractive indices corresponding to three principal axes of the crystal. For most ray directions, both polarizations would be classified as extraordinary rays but with different effective refractive indices, being extraordinary waves, however, the direction of power flow is not identical to the direction of the wave vector in either case. The two refractive indices can be determined using the index ellipsoids for given directions of the polarization, note that for biaxial crystals the index ellipsoid will not be an ellipsoid of revolution but is described by three unequal principle refractive indices nα, nβ and nγ. Thus there is no axis around which a rotation leaves the optical properties invariant, for this reason, birefringent materials with three distinct refractive indices are called biaxial

23.
Dichroism
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The original meaning of dichroic, from the Greek dikhroos, two-coloured, refers to any optical device which can split a beam of light into two beams with differing wavelengths. This kind of dichroic device does not usually depend on the polarization of the light, the term dichromatic is also used in this sense. When the polarization states in question are right and left-handed circular polarization and this is more generally referred to as pleochroism, and the technique can be used in mineralogy to identify minerals. In some materials, such as herapathite or Polaroid sheets, the effect is not strongly dependent on wavelength. Dichroism, in the second meaning above, occurs in liquid crystals due to either the optical anisotropy of the structure or the presence of impurities or the presence of dichroic dyes. The latter is called a guest–host effect

24.
Optical rotation
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Optical rotation or optical activity is the rotation of the plane of polarization of linearly polarized light as it travels through certain materials. Optical activity occurs only in chiral materials, those lacking microscopic mirror symmetry, unlike other sources of birefringence which alter a beams state of polarization, optical activity can be observed in fluids. This can include gases or solutions of chiral molecules such as sugars, molecules with helical secondary structure such as some proteins and it can also be observed in chiral solids such as certain crystals with a rotation between adjacent crystal planes or metamaterials. The rotation of the plane of polarization may be either clockwise, to the right, for instance, sucrose and camphor are d-rotary whereas cholesterol is l-rotary. For a given substance, the angle by which the polarization of light of a wavelength is rotated is proportional to the path length through the material and proportional to its concentration. The rotation is not dependent on the direction of propagation, unlike the Faraday effect where the rotation is dependent on the direction of the applied magnetic field. Optical activity is measured using a source and polarimeter. Modulation of a liquid crystals optical activity, viewed between two polarizers, is the principle of operation of liquid-crystal displays. The rotation of the orientation of polarized light was first observed in 1811 in quartz by French physicist François Jean Dominique Arago. Jean Baptiste Biot also observed the rotation of the axis of polarization in certain liquids, simple polarimeters have been used since this time to measure the concentrations of simple sugars, such as glucose, in solution. In fact one name for D-glucose, is dextrose, referring to the fact that it causes linearly polarized light to rotate to the right or dexter side. In a similar manner, levulose, more known as fructose. Fructose is even more strongly levorotatory than glucose is dextrorotatory, in 1849, Louis Pasteur resolved a problem concerning the nature of tartaric acid. Pasteur noticed that the crystals come in two forms that are mirror images of one another. Sorting the crystals by hand gave two forms of the compound, Solutions of one form rotate polarized light clockwise, while the other form rotate light counterclockwise, an equal mix of the two has no polarizing effect on light. If the 4 neighbors are all different, then there are two possible orderings of the neighbors around the tetrahedron, which will be mirror images of each other and this led to a better understanding of the three-dimensional nature of molecules. Optical activity occurs due to molecules dissolved in a fluid or due to the fluid itself only if the molecules are one of two stereoisomers, this is known as an enantiomer, the structure of such a molecule is such that it is not identical to its mirror image. In mathematics, this property is known as chirality

25.
Quantum mechanics
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Quantum mechanics, including quantum field theory, is a branch of physics which is the fundamental theory of nature at small scales and low energies of atoms and subatomic particles. Classical physics, the physics existing before quantum mechanics, derives from quantum mechanics as an approximation valid only at large scales, early quantum theory was profoundly reconceived in the mid-1920s. The reconceived theory is formulated in various specially developed mathematical formalisms, in one of them, a mathematical function, the wave function, provides information about the probability amplitude of position, momentum, and other physical properties of a particle. In 1803, Thomas Young, an English polymath, performed the famous experiment that he later described in a paper titled On the nature of light. This experiment played a role in the general acceptance of the wave theory of light. In 1838, Michael Faraday discovered cathode rays, Plancks hypothesis that energy is radiated and absorbed in discrete quanta precisely matched the observed patterns of black-body radiation. In 1896, Wilhelm Wien empirically determined a distribution law of black-body radiation, ludwig Boltzmann independently arrived at this result by considerations of Maxwells equations. However, it was only at high frequencies and underestimated the radiance at low frequencies. Later, Planck corrected this model using Boltzmanns statistical interpretation of thermodynamics and proposed what is now called Plancks law, following Max Plancks solution in 1900 to the black-body radiation problem, Albert Einstein offered a quantum-based theory to explain the photoelectric effect. Among the first to study quantum phenomena in nature were Arthur Compton, C. V. Raman, robert Andrews Millikan studied the photoelectric effect experimentally, and Albert Einstein developed a theory for it. In 1913, Peter Debye extended Niels Bohrs theory of structure, introducing elliptical orbits. This phase is known as old quantum theory, according to Planck, each energy element is proportional to its frequency, E = h ν, where h is Plancks constant. Planck cautiously insisted that this was simply an aspect of the processes of absorption and emission of radiation and had nothing to do with the reality of the radiation itself. In fact, he considered his quantum hypothesis a mathematical trick to get the right rather than a sizable discovery. He won the 1921 Nobel Prize in Physics for this work, lower energy/frequency means increased time and vice versa, photons of differing frequencies all deliver the same amount of action, but do so in varying time intervals. High frequency waves are damaging to human tissue because they deliver their action packets concentrated in time, the Copenhagen interpretation of Niels Bohr became widely accepted. In the mid-1920s, developments in mechanics led to its becoming the standard formulation for atomic physics. In the summer of 1925, Bohr and Heisenberg published results that closed the old quantum theory, out of deference to their particle-like behavior in certain processes and measurements, light quanta came to be called photons

26.
Photon
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A photon is an elementary particle, the quantum of the electromagnetic field including electromagnetic radiation such as light, and the force carrier for the electromagnetic force. The photon has zero rest mass and is moving at the speed of light. Like all elementary particles, photons are currently best explained by quantum mechanics and exhibit wave–particle duality, exhibiting properties of both waves and particles. For example, a photon may be refracted by a lens and exhibit wave interference with itself. The quanta in a light wave cannot be spatially localized, some defined physical parameters of a photon are listed. The modern concept of the photon was developed gradually by Albert Einstein in the early 20th century to explain experimental observations that did not fit the classical model of light. The benefit of the model was that it accounted for the frequency dependence of lights energy. The photon model accounted for observations, including the properties of black-body radiation. In that model, light was described by Maxwells equations, in 1926 the optical physicist Frithiof Wolfers and the chemist Gilbert N. Lewis coined the name photon for these particles. After Arthur H. Compton won the Nobel Prize in 1927 for his studies, most scientists accepted that light quanta have an independent existence. In the Standard Model of particle physics, photons and other particles are described as a necessary consequence of physical laws having a certain symmetry at every point in spacetime. The intrinsic properties of particles, such as charge, mass and it has been applied to photochemistry, high-resolution microscopy, and measurements of molecular distances. Recently, photons have been studied as elements of quantum computers, in 1900, the German physicist Max Planck was studying black-body radiation and suggested that the energy carried by electromagnetic waves could only be released in packets of energy. In his 1901 article in Annalen der Physik he called these packets energy elements, the word quanta was used before 1900 to mean particles or amounts of different quantities, including electricity. In 1905, Albert Einstein suggested that waves could only exist as discrete wave-packets. He called such a wave-packet the light quantum, the name photon derives from the Greek word for light, φῶς. Arthur Compton used photon in 1928, referring to Gilbert N. Lewis, the name was suggested initially as a unit related to the illumination of the eye and the resulting sensation of light and was used later in a physiological context. Although Wolferss and Lewiss theories were contradicted by many experiments and never accepted, in physics, a photon is usually denoted by the symbol γ

27.
Spin (physics)
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In quantum mechanics and particle physics, spin is an intrinsic form of angular momentum carried by elementary particles, composite particles, and atomic nuclei. Spin is one of two types of angular momentum in mechanics, the other being orbital angular momentum. In some ways, spin is like a vector quantity, it has a definite magnitude, all elementary particles of a given kind have the same magnitude of spin angular momentum, which is indicated by assigning the particle a spin quantum number. The SI unit of spin is the or, just as with classical angular momentum, very often, the spin quantum number is simply called spin leaving its meaning as the unitless spin quantum number to be inferred from context. When combined with the theorem, the spin of electrons results in the Pauli exclusion principle. Wolfgang Pauli was the first to propose the concept of spin, in 1925, Ralph Kronig, George Uhlenbeck and Samuel Goudsmit at Leiden University suggested an physical interpretation of particles spinning around their own axis. The mathematical theory was worked out in depth by Pauli in 1927, when Paul Dirac derived his relativistic quantum mechanics in 1928, electron spin was an essential part of it. As the name suggests, spin was originally conceived as the rotation of a particle around some axis and this picture is correct so far as spin obeys the same mathematical laws as quantized angular momenta do. On the other hand, spin has some properties that distinguish it from orbital angular momenta. Although the direction of its spin can be changed, a particle cannot be made to spin faster or slower. The spin of a particle is associated with a magnetic dipole moment with a g-factor differing from 1. This could only occur if the internal charge of the particle were distributed differently from its mass. The conventional definition of the quantum number, s, is s = n/2. Hence the allowed values of s are 0, 1/2,1, 3/2,2, the value of s for an elementary particle depends only on the type of particle, and cannot be altered in any known way. The spin angular momentum, S, of any system is quantized. The allowed values of S are S = ℏ s = h 4 π n, in contrast, orbital angular momentum can only take on integer values of s, i. e. even-numbered values of n. Those particles with half-integer spins, such as 1/2, 3/2, 5/2, are known as fermions, while particles with integer spins. The two families of particles obey different rules and broadly have different roles in the world around us, a key distinction between the two families is that fermions obey the Pauli exclusion principle, that is, there cannot be two identical fermions simultaneously having the same quantum numbers

28.
Optics
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Optics is the branch of physics which involves the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviolet, and infrared light, because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties. Most optical phenomena can be accounted for using the classical description of light. Complete electromagnetic descriptions of light are, however, often difficult to apply in practice, practical optics is usually done using simplified models. The most common of these, geometric optics, treats light as a collection of rays that travel in straight lines, physical optics is a more comprehensive model of light, which includes wave effects such as diffraction and interference that cannot be accounted for in geometric optics. Historically, the model of light was developed first, followed by the wave model of light. Progress in electromagnetic theory in the 19th century led to the discovery that waves were in fact electromagnetic radiation. Some phenomena depend on the fact that light has both wave-like and particle-like properties, explanation of these effects requires quantum mechanics. When considering lights particle-like properties, the light is modelled as a collection of particles called photons, quantum optics deals with the application of quantum mechanics to optical systems. Optical science is relevant to and studied in many related disciplines including astronomy, various engineering fields, photography, practical applications of optics are found in a variety of technologies and everyday objects, including mirrors, lenses, telescopes, microscopes, lasers, and fibre optics. Optics began with the development of lenses by the ancient Egyptians and Mesopotamians, the earliest known lenses, made from polished crystal, often quartz, date from as early as 700 BC for Assyrian lenses such as the Layard/Nimrud lens. The ancient Romans and Greeks filled glass spheres with water to make lenses, the word optics comes from the ancient Greek word ὀπτική, meaning appearance, look. Greek philosophy on optics broke down into two opposing theories on how vision worked, the theory and the emission theory. The intro-mission approach saw vision as coming from objects casting off copies of themselves that were captured by the eye, plato first articulated the emission theory, the idea that visual perception is accomplished by rays emitted by the eyes. He also commented on the parity reversal of mirrors in Timaeus, some hundred years later, Euclid wrote a treatise entitled Optics where he linked vision to geometry, creating geometrical optics. Ptolemy, in his treatise Optics, held a theory of vision, the rays from the eye formed a cone, the vertex being within the eye. The rays were sensitive, and conveyed back to the observer’s intellect about the distance. He summarised much of Euclid and went on to describe a way to measure the angle of refraction, during the Middle Ages, Greek ideas about optics were resurrected and extended by writers in the Muslim world

29.
Seismology
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Seismology is the scientific study of earthquakes and the propagation of elastic waves through the Earth or through other planet-like bodies. A related field that uses geology to infer information regarding past earthquakes is paleoseismology, a recording of earth motion as a function of time is called a seismogram. A seismologist is a scientist who does research in seismology, scholarly interest in earthquakes can be traced back to antiquity. Early speculations on the causes of earthquakes were included in the writings of Thales of Miletus, Anaximenes of Miletus, Aristotle. In 132 CE, Zhang Heng of Chinas Han dynasty designed the first known seismoscope, in 1664, Athanasius Kircher argued that earthquakes were caused by the movement of fire within a system of channels inside the Earth. In 1703, Martin Lister and Nicolas Lemery proposed that earthquakes were caused by chemical explosions within the earth, the Lisbon earthquake of 1755, coinciding with the general flowering of science in Europe, set in motion intensified scientific attempts to understand the behaviour and causation of earthquakes. The earliest responses include work by John Bevis and John Michell, Michell determined that earthquakes originate within the Earth and were waves of movement caused by shifting masses of rock miles below the surface. From 1857, Robert Mallet laid the foundation of instrumental seismology and he is also responsible for coining the word seismology. In 1897, Emil Wiecherts theoretical calculations led him to conclude that the Earths interior consists of a mantle of silicates, surrounding a core of iron. In 1906 Richard Dixon Oldham identified the separate arrival of P-waves, S-waves and surface waves on seismograms, in 1910, after studying the 1906 San Francisco earthquake, Harry Fielding Reid put forward the elastic rebound theory which remains the foundation for modern tectonic studies. The development of this depended on the considerable progress of earlier independent streams of work on the behaviour of elastic materials. In 1926, Harold Jeffreys was the first to claim, based on his study of waves, that below the mantle. In 1937, Inge Lehmann determined that within the liquid outer core there is a solid inner core. By the 1960s, earth science had developed to the point where a comprehensive theory of the causation of seismic events had come together in the now well-established theory of plate tectonics, seismic waves are elastic waves that propagate in solid or fluid materials. There are two types of waves, Pressure waves or Primary waves and Shear or Secondary waves. S-waves are transverse waves that move perpendicular to the direction of propagation, therefore, they appear later than P-waves on a seismogram. Fluids cannot support perpendicular motion, so S-waves only travel in solids, the two main surface wave types are Rayleigh waves, which have some compressional motion, and Love waves, which do not. Rayleigh waves result from the interaction of vertically polarized P- and S-waves that satisfy the conditions on the surface

30.
Radio
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When radio waves strike an electrical conductor, the oscillating fields induce an alternating current in the conductor. The information in the waves can be extracted and transformed back into its original form, Radio systems need a transmitter to modulate some property of the energy produced to impress a signal on it, for example using amplitude modulation or angle modulation. Radio systems also need an antenna to convert electric currents into radio waves, an antenna can be used for both transmitting and receiving. The electrical resonance of tuned circuits in radios allow individual stations to be selected, the electromagnetic wave is intercepted by a tuned receiving antenna. Radio frequencies occupy the range from a 3 kHz to 300 GHz, a radio communication system sends signals by radio. The term radio is derived from the Latin word radius, meaning spoke of a wheel, beam of light, however, this invention would not be widely adopted. The switch to radio in place of wireless took place slowly and unevenly in the English-speaking world, the United States Navy would also play a role. Although its translation of the 1906 Berlin Convention used the terms wireless telegraph and wireless telegram, the term started to become preferred by the general public in the 1920s with the introduction of broadcasting. Radio systems used for communication have the following elements, with more than 100 years of development, each process is implemented by a wide range of methods, specialised for different communications purposes. Each system contains a transmitter, This consists of a source of electrical energy, the transmitter contains a system to modulate some property of the energy produced to impress a signal on it. This modulation might be as simple as turning the energy on and off, or altering more subtle such as amplitude, frequency, phase. Amplitude modulation of a carrier wave works by varying the strength of the signal in proportion to the information being sent. For example, changes in the strength can be used to reflect the sounds to be reproduced by a speaker. It was the used for the first audio radio transmissions. Frequency modulation varies the frequency of the carrier, the instantaneous frequency of the carrier is directly proportional to the instantaneous value of the input signal. FM has the capture effect whereby a receiver only receives the strongest signal, Digital data can be sent by shifting the carriers frequency among a set of discrete values, a technique known as frequency-shift keying. FM is commonly used at Very high frequency radio frequencies for high-fidelity broadcasts of music, analog TV sound is also broadcast using FM. Angle modulation alters the phase of the carrier wave to transmit a signal

31.
Microwave
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Microwaves are a form of electromagnetic radiation with wavelengths ranging from one meter to one millimeter, with frequencies between 300 MHz and 300 GHz. Different sources define different frequency ranges as microwaves, the broad definition includes both UHF and EHF bands. A more common definition in radio engineering is the range between 1 and 100 GHz, in all cases, microwaves include the entire SHF band at minimum. Frequencies in the range are often referred to by their IEEE radar band designations, S, C, X, Ku, K, or Ka band. The prefix micro- in microwave is not meant to suggest a wavelength in the micrometer range and it indicates that microwaves are small, compared to waves used in typical radio broadcasting, in that they have shorter wavelengths. The boundaries between far infrared, terahertz radiation, microwaves, and ultra-high-frequency radio waves are fairly arbitrary and are used variously between different fields of study. At the high end of the band they are absorbed by gases in the atmosphere, microwaves are extremely widely used in modern technology. Although at the low end of the band they can pass through building walls enough for useful reception, therefore on the surface of the Earth microwave communication links are limited by the visual horizon to about 30 -40 miles. Microwaves are absorbed by moisture in the atmosphere, and the attenuation increases with frequency, beginning at about 40 GHz, atmospheric gases also begin to absorb microwaves, so above this frequency microwave transmission is limited to a few kilometers. A spectral band structure causes absorption peaks at specific frequencies, in a microwave beam directed at an angle into the sky, a small amount of the power will be randomly scattered as the beam passes through the troposphere. A sensitive receiver beyond the horizon with a high gain antenna focused on that area of the troposphere can pick up the signal. This technique has been used at frequencies between 0.45 and 5 GHz in tropospheric scatter communication systems to communicate beyond the horizon and their short wavelength allows narrow beams of microwaves to be produced by conveniently small high gain antennas from a half meter to 5 meters in diameter. Therefore beams of microwaves are used for point-to-point communication links, an advantage of narrow beams is that they allow frequency reuse by nearby transmitters. Parabolic antennas are the most widely used directive antennas at microwave frequencies, flat microstrip antennas are being increasingly used in consumer devices. Where omnidirectional antennas are required, for example in wireless devices and Wifi routers for wireless LANs, small monopoles, dipole, or patch antennas are used. Due to the high cost and maintenance requirements of waveguide runs, the term microwave also has a more technical meaning in electromagnetics and circuit theory. As a consequence, practical microwave circuits tend to away from the discrete resistors, capacitors. Open-wire and coaxial transmission lines used at lower frequencies are replaced by waveguides and stripline, high-power microwave sources use specialized vacuum tubes to generate microwaves

32.
Laser
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A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The term laser originated as an acronym for light amplification by stimulated emission of radiation, the first laser was built in 1960 by Theodore H. Maiman at Hughes Research Laboratories, based on theoretical work by Charles Hard Townes and Arthur Leonard Schawlow. A laser differs from other sources of light in that it emits light coherently, spatial coherence allows a laser to be focused to a tight spot, enabling applications such as laser cutting and lithography. Spatial coherence also allows a laser beam to stay narrow over great distances, Lasers can also have high temporal coherence, which allows them to emit light with a very narrow spectrum, i. e. they can emit a single color of light. Temporal coherence can be used to produce pulses of light as short as a femtosecond, Lasers are distinguished from other light sources by their coherence. Spatial coherence is typically expressed through the output being a narrow beam, Laser beams can be focused to very tiny spots, achieving a very high irradiance, or they can have very low divergence in order to concentrate their power at a great distance. Temporal coherence implies a polarized wave at a single frequency whose phase is correlated over a great distance along the beam. A beam produced by a thermal or other incoherent light source has an amplitude and phase that vary randomly with respect to time and position. Lasers are characterized according to their wavelength in a vacuum, most single wavelength lasers actually produce radiation in several modes having slightly differing frequencies, often not in a single polarization. Although temporal coherence implies monochromaticity, there are lasers that emit a broad spectrum of light or emit different wavelengths of light simultaneously, there are some lasers that are not single spatial mode and consequently have light beams that diverge more than is required by the diffraction limit. However, all devices are classified as lasers based on their method of producing light. Lasers are employed in applications where light of the spatial or temporal coherence could not be produced using simpler technologies. The word laser started as an acronym for light amplification by stimulated emission of radiation, in the early technical literature, especially at Bell Telephone Laboratories, the laser was called an optical maser, this term is now obsolete. A laser that produces light by itself is technically an optical rather than an optical amplifier as suggested by the acronym. It has been noted that the acronym LOSER, for light oscillation by stimulated emission of radiation. With the widespread use of the acronym as a common noun, optical amplifiers have come to be referred to as laser amplifiers. The back-formed verb to lase is frequently used in the field, meaning to produce light, especially in reference to the gain medium of a laser. Further use of the laser and maser in an extended sense, not referring to laser technology or devices, can be seen in usages such as astrophysical maser

33.
Telecommunication
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Telecommunication is the transmission of signs, signals, messages, writings, images and sounds or intelligence of any nature by wire, radio, optical or other electromagnetic systems. Telecommunication occurs when the exchange of information between communication participants includes the use of technology and it is transmitted either electrically over physical media, such as cables, or via electromagnetic radiation. Such transmission paths are divided into communication channels which afford the advantages of multiplexing. The term is used in its plural form, telecommunications. Early means of communicating over a distance included visual signals, such as beacons, smoke signals, semaphore telegraphs, signal flags, other examples of pre-modern long-distance communication included audio messages such as coded drumbeats, lung-blown horns, and loud whistles. Zworykin, John Logie Baird and Philo Farnsworth, the word telecommunication is a compound of the Greek prefix tele, meaning distant, far off, or afar, and the Latin communicare, meaning to share. Its modern use is adapted from the French, because its use was recorded in 1904 by the French engineer. Communication was first used as an English word in the late 14th century, in the Middle Ages, chains of beacons were commonly used on hilltops as a means of relaying a signal. Beacon chains suffered the drawback that they could pass a single bit of information. One notable instance of their use was during the Spanish Armada, in 1792, Claude Chappe, a French engineer, built the first fixed visual telegraphy system between Lille and Paris. However semaphore suffered from the need for skilled operators and expensive towers at intervals of ten to thirty kilometres, as a result of competition from the electrical telegraph, the last commercial line was abandoned in 1880. Homing pigeons have occasionally used throughout history by different cultures. Pigeon post is thought to have Persians roots and was used by the Romans to aid their military, frontinus said that Julius Caesar used pigeons as messengers in his conquest of Gaul. The Greeks also conveyed the names of the victors at the Olympic Games to various cities using homing pigeons, in the early 19th century, the Dutch government used the system in Java and Sumatra. And in 1849, Paul Julius Reuter started a service to fly stock prices between Aachen and Brussels, a service that operated for a year until the gap in the telegraph link was closed. Sir Charles Wheatstone and Sir William Fothergill Cooke invented the telegraph in 1837. Also, the first commercial electrical telegraph is purported to have constructed by Wheatstone and Cooke. Both inventors viewed their device as an improvement to the electromagnetic telegraph not as a new device, samuel Morse independently developed a version of the electrical telegraph that he unsuccessfully demonstrated on 2 September 1837

34.
Radar
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Radar is an object-detection system that uses radio waves to determine the range, angle, or velocity of objects. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, weather formations, Radio waves from the transmitter reflect off the object and return to the receiver, giving information about the objects location and speed. Radar was developed secretly for military use by several nations in the period before, the term RADAR was coined in 1940 by the United States Navy as an acronym for RAdio Detection And Ranging or RAdio Direction And Ranging. The term radar has since entered English and other languages as a common noun, high tech radar systems are associated with digital signal processing, machine learning and are capable of extracting useful information from very high noise levels. Other systems similar to make use of other parts of the electromagnetic spectrum. One example is lidar, which uses ultraviolet, visible, or near infrared light from lasers rather than radio waves, as early as 1886, German physicist Heinrich Hertz showed that radio waves could be reflected from solid objects. In 1895, Alexander Popov, an instructor at the Imperial Russian Navy school in Kronstadt. The next year, he added a spark-gap transmitter, in 1897, while testing this equipment for communicating between two ships in the Baltic Sea, he took note of an interference beat caused by the passage of a third vessel. In his report, Popov wrote that this phenomenon might be used for detecting objects, the German inventor Christian Hülsmeyer was the first to use radio waves to detect the presence of distant metallic objects. In 1904, he demonstrated the feasibility of detecting a ship in dense fog and he obtained a patent for his detection device in April 1904 and later a patent for a related amendment for estimating the distance to the ship. He also got a British patent on September 23,1904 for a radar system. It operated on a 50 cm wavelength and the radar signal was created via a spark-gap. In 1915, Robert Watson-Watt used radio technology to advance warning to airmen. Watson-Watt became an expert on the use of direction finding as part of his lightning experiments. As part of ongoing experiments, he asked the new boy, Arnold Frederic Wilkins, Wilkins made an extensive study of available units before selecting a receiver model from the General Post Office. Its instruction manual noted that there was fading when aircraft flew by, in 1922, A. Hoyt Taylor and Leo C. Taylor submitted a report, suggesting that this might be used to detect the presence of ships in low visibility, eight years later, Lawrence A. Australia, Canada, New Zealand, and South Africa followed prewar Great Britain, and Hungary had similar developments during the war. Hugon, began developing a radio apparatus, a part of which was installed on the liner Normandie in 1935

35.
Plane wave
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In the physics of wave propagation, a plane wave is a wave whose wavefronts are infinite parallel planes. The solutions in x → of n → c ⋅ x → − t = c o n s t. comprise the plane with normal vector n →, thus, the points of equal field value of A always form a plane in space. This plane then shifts with time t, along the direction of propagation n → with velocity c, the term is often used to mean the special case of a monochromatic, homogeneous plane wave. A monochromatic plane wave is one in which the amplitude is a function of x and t. A homogeneous plane wave is one in which the planes of constant phase are perpendicular to the direction of propagation n →, however, many waves are approximately plane waves in a localized region of space. For example, a source such as an antenna produces a field that is approximately a plane wave far from the antenna in its far-field region. Two functions that meet the criteria of having a constant frequency. One of the simplest ways to use such a sinusoid involves defining it along the direction of the x-axis, the equation below, which is illustrated toward the right, uses the cosine function to represent a harmonic and homogeneous plane wave travelling in the positive x direction. A = A o cos ⁡ In the above equation, A is the magnitude or disturbance of the wave at a point in space. An example would be to let A represent the variation of air pressure relative to the norm in the case of a sound wave, a o is the amplitude of the wave which is the peak magnitude of the oscillation. K is the wave number or more specifically the angular wave number and equals 2π/λ. K has the units of radians per unit distance and is a measure of how rapidly the disturbance changes over a distance at a particular point in time. X is a point along the x-axis, Y and z are not part of the equation because the waves magnitude and phase are the same at every point on any given y-z plane. This equation defines what that magnitude and phase are, ω is the wave’s angular frequency which equals 2π/T, where T is the period of the wave. ω has the units of radians per unit time and is a measure of how rapidly the disturbance changes over a length of time at a particular point in space. T is a point in time φ is the phase shift of the wave and has the units of radians. Note that a phase shift, at a given moment of time. A phase shift of 2π radians shifts it exactly one wavelength, other formalisms which directly use the wave’s wavelength λ, period T, frequency f and velocity c are below

36.
Wave vector
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In physics, a wave vector is a vector which helps describe a wave. In the context of relativity the wave vector can also be defined as a four-vector. There are two definitions of wave vector, which differ by a factor of 2π in their magnitudes. One definition is preferred in physics and related fields, while the definition is preferred in crystallography. For this article, they will be called the physics definition, a perfect one-dimensional traveling wave follows the equation, ψ = A cos ⁡ where, x is position, t is time, ψ is the disturbance describing the wave. This wave travels in the +x direction with speed ω / k, in crystallography, the same waves are described using slightly different equations. In one and three respectively, ψ = A cos ⁡ ψ = A cos ⁡ The differences are. They are related by 2 π ν = ω and this substitution is not important for this article, but reflects common practice in crystallography. The wavenumber k and wave vector k are defined in a different way, here, k = | k | =1 / λ, while in the physics definition above, k = | k | =2 π / λ. The direction of k is discussed below, the direction in which the wave vector points must be distinguished from the direction of wave propagation. The direction of propagation is the direction of a waves energy flow. For light waves, this is also the direction of the Poynting vector, on the other hand, the wave vector points in the direction of phase velocity. In other words, the vector points in the normal direction to the surfaces of constant phase. In a lossless isotropic medium such as air, any gas, any liquid, or some solids, if the medium is lossy, the wave vector in general points in directions other than that of wave propagation. The condition for wave vector to point in the direction in which the wave propagates is that the wave has to be homogeneous. In a homogeneous wave, the surfaces of constant phase are also surfaces of constant amplitude, in case of inhomogeneous waves, these two species of surfaces differ in orientation. Wave vector is perpendicular to surfaces of constant phase. In solid-state physics, the wavevector of an electron or hole in a crystal is the wavevector of its quantum-mechanical wavefunction, see Bloch wave for further details

37.
Probability distribution
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For instance, if the random variable X is used to denote the outcome of a coin toss, then the probability distribution of X would take the value 0.5 for X = heads, and 0.5 for X = tails. In more technical terms, the probability distribution is a description of a phenomenon in terms of the probabilities of events. Examples of random phenomena can include the results of an experiment or survey, a probability distribution is defined in terms of an underlying sample space, which is the set of all possible outcomes of the random phenomenon being observed. The sample space may be the set of numbers or a higher-dimensional vector space, or it may be a list of non-numerical values, for example. Probability distributions are divided into two classes. A discrete probability distribution can be encoded by a discrete list of the probabilities of the outcomes, on the other hand, a continuous probability distribution is typically described by probability density functions. The normal distribution represents a commonly encountered continuous probability distribution, more complex experiments, such as those involving stochastic processes defined in continuous time, may demand the use of more general probability measures. A probability distribution whose sample space is the set of numbers is called univariate. Important and commonly encountered univariate probability distributions include the distribution, the hypergeometric distribution. The multivariate normal distribution is a commonly encountered multivariate distribution, to define probability distributions for the simplest cases, one needs to distinguish between discrete and continuous random variables. For example, the probability that an object weighs exactly 500 g is zero. Continuous probability distributions can be described in several ways, the cumulative distribution function is the antiderivative of the probability density function provided that the latter function exists. As probability theory is used in diverse applications, terminology is not uniform. The following terms are used for probability distribution functions, Distribution. Probability distribution, is a table that displays the probabilities of outcomes in a sample. Could be called a frequency distribution table, where all occurrences of outcomes sum to 1. Distribution function, is a form of frequency distribution table. Probability distribution function, is a form of probability distribution table

38.
Spectral density
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The power spectrum S x x of a time series x describes the distribution of power into frequency components composing that signal. According to Fourier analysis any physical signal can be decomposed into a number of discrete frequencies, the statistical average of a certain signal or sort of signal as analyzed in terms of its frequency content, is called its spectrum. When the energy of the signal is concentrated around a time interval, especially if its total energy is finite. More commonly used is the spectral density, which applies to signals existing over all time. The power spectral density then refers to the energy distribution that would be found per unit time. Summation or integration of the spectral components yields the total power or variance, identical to what would be obtained by integrating x 2 over the time domain, the spectrum of a physical process x often contains essential information about the nature of x. For instance, the pitch and timbre of an instrument are immediately determined from a spectral analysis. The color of a source is determined by the spectrum of the electromagnetic waves electric field E as it fluctuates at an extremely high frequency. Obtaining a spectrum from time series such as these involves the Fourier transform, however this article concentrates on situations in which the time series is known or directly measured. The power spectrum is important in signal processing and in the statistical study of stochastic processes, as well as in many other branches of physics. Typically the process is a function of time but one can similarly discuss data in the domain being decomposed in terms of spatial frequency. Any signal that can be represented as an amplitude that varies in time has a frequency spectrum. This includes familiar entities such as light, musical notes, radio/TV. When these signals are viewed in the form of a frequency spectrum, in some cases the frequency spectrum may include a distinct peak corresponding to a sine wave component. And additionally there may be corresponding to harmonics of a fundamental peak. In physics, the signal might be a wave, such as an electromagnetic wave, the power spectral density of the signal describes the power present in the signal as a function of frequency, per unit frequency. Power spectral density is expressed in watts per hertz. When a signal is defined in terms only of a voltage, for instance, in this case power is simply reckoned in terms of the square of the signal, as this would always be proportional to the actual power delivered by that signal into a given impedance

39.
Attenuation
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In physics, attenuation is the gradual loss in intensity of any kind of flux through a medium. For instance, dark glasses attenuate sunlight, lead attenuates X-rays, in electrical engineering and telecommunications, attenuation affects the propagation of waves and signals in electrical circuits, in optical fibers, and in air. Electrical attenuators and optical attenuators are commonly manufactured components in this field, in many cases, attenuation is an exponential function of the path length through the medium. In chemical spectroscopy, this is known as the Beer–Lambert law, in engineering, attenuation is usually measured in units of decibels per unit length of medium and is represented by the attenuation coefficient of the medium in question. Attenuation also occurs in earthquakes, when the waves move farther away from the epicenter. One area of research in which figures strongly is in ultrasound physics. Attenuation in ultrasound is the reduction in amplitude of the beam as a function of distance through the imaging medium. Accounting for attenuation effects in ultrasound is important because a reduced signal amplitude can affect the quality of the image produced. By knowing the attenuation that an ultrasound beam experiences traveling through a medium, ultrasound attenuation measurement in heterogeneous systems, like emulsions or colloids, yields information on particle size distribution. There is an ISO standard on this technique, ultrasound attenuation can be used for extensional rheology measurement. There are acoustic rheometers that employ Stokes law for measuring extensional viscosity, wave equations which take acoustic attenuation into account can be written on a fractional derivative form, see the article on acoustic attenuation or e. g. the survey paper. Attenuation coefficients are used to different media according to how strongly the transmitted ultrasound amplitude decreases as a function of frequency. Attenuation coefficients vary widely for different media, in biomedical ultrasound imaging however, biological materials and water are the most commonly used media. Ultrasound propagation through homogeneous media is associated only with absorption and can be characterized with absorption coefficient only, propagation through heterogeneous media requires taking into account scattering. When the sun’s radiation reaches the sea-surface, the radiation is attenuated by the water. The intensity of light at depth can be calculated using the Beer-Lambert Law, in clear open waters, visible light is absorbed at the longest wavelengths first. Thus, red, orange, and yellow wavelengths are absorbed at higher water depths, because the blue and violet wavelengths are absorbed last compared to the other wavelengths, open ocean waters appear deep-blue to the eye. In near-shore waters, sea water contains more phytoplankton than the very clear central ocean waters, chlorophyll-a pigments in the phytoplankton absorb light, and the plants themselves scatter light, making coastal waters less clear than open waters

40.
Complex number
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A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, satisfying the equation i2 = −1. In this expression, a is the part and b is the imaginary part of the complex number. If z = a + b i, then ℜ z = a, ℑ z = b, Complex numbers extend the concept of the one-dimensional number line to the two-dimensional complex plane by using the horizontal axis for the real part and the vertical axis for the imaginary part. The complex number a + bi can be identified with the point in the complex plane, a complex number whose real part is zero is said to be purely imaginary, whereas a complex number whose imaginary part is zero is a real number. In this way, the numbers are a field extension of the ordinary real numbers. As well as their use within mathematics, complex numbers have applications in many fields, including physics, chemistry, biology, economics, electrical engineering. The Italian mathematician Gerolamo Cardano is the first known to have introduced complex numbers and he called them fictitious during his attempts to find solutions to cubic equations in the 16th century. Complex numbers allow solutions to equations that have no solutions in real numbers. For example, the equation 2 = −9 has no real solution, Complex numbers provide a solution to this problem. The idea is to extend the real numbers with the unit i where i2 = −1. According to the theorem of algebra, all polynomial equations with real or complex coefficients in a single variable have a solution in complex numbers. A complex number is a number of the form a + bi, for example, −3.5 + 2i is a complex number. The real number a is called the part of the complex number a + bi. By this convention the imaginary part does not include the unit, hence b. The real part of a number z is denoted by Re or ℜ. For example, Re ⁡ = −3.5 Im ⁡ =2, hence, in terms of its real and imaginary parts, a complex number z is equal to Re ⁡ + Im ⁡ ⋅ i. This expression is known as the Cartesian form of z. A real number a can be regarded as a number a + 0i whose imaginary part is 0

41.
Phasor
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In physics and engineering, a phasor, is a complex number representing a sinusoidal function whose amplitude, angular frequency, and initial phase are time-invariant. The complex constant, which encapsulates amplitude and phase dependence, is known as phasor, complex amplitude, a common situation in electrical networks is the existence of multiple sinusoids all with the same frequency, but different amplitudes and phases. The only difference in their analytic representations is the complex amplitude, a linear combination of such functions can be factored into the product of a linear combination of phasors and the time/frequency dependent factor that they all have in common. The origin of the term phasor rightfully suggests that a somewhat similar to that possible for vectors is possible for phasors as well. The originator of the phasor transform was Charles Proteus Steinmetz working at General Electric in the late 19th century, however, the Laplace transform is mathematically more difficult to apply and the effort may be unjustified if only steady state analysis is required. The function A ⋅ e i is the representation of A ⋅ cos ⁡. Figure 2 depicts it as a vector in a complex plane. It is sometimes convenient to refer to the function as a phasor. But the term usually implies just the static vector, A e i θ. An even more compact representation of a phasor is the angle notation, multiplication of the phasor A e i θ e i ω t by a complex constant, B e i ϕ, produces another phasor. That means its only effect is to change the amplitude and phase of the underlying sinusoid, Re ⁡ = Re ⁡ = A B cos ⁡ In electronics, B e i ϕ would represent an impedance, in particular it is not the shorthand notation for another phasor. Multiplying a phasor current by an impedance produces a phasor voltage, but the product of two phasors would represent the product of two sinusoids, which is a non-linear operation that produces new frequency components. Phasor notation can only represent systems with one frequency, such as a linear system stimulated by a sinusoid, the time derivative or integral of a phasor produces another phasor. For example, Re ⁡ = Re ⁡ = Re ⁡ = Re ⁡ = ω A ⋅ cos ⁡ Therefore, in phasor representation, similarly, integrating a phasor corresponds to multiplication by 1 i ω = e − i π /2 ω. The time-dependent factor, e i ω t, is unaffected, when we solve a linear differential equation with phasor arithmetic, we are merely factoring e i ω t out of all terms of the equation, and reinserting it into the answer. In polar coordinate form, it is,11 +2 ⋅ e − i ϕ, Therefore, v C =11 +2 ⋅ V P cos ⁡ The sum of multiple phasors produces another phasor. A key point is that A3 and θ3 do not depend on ω or t, the time and frequency dependence can be suppressed and re-inserted into the outcome as long as the only operations used in between are ones that produce another phasor. In angle notation, the operation shown above is written, A1 ∠ θ1 + A2 ∠ θ2 = A3 ∠ θ3, another way to view addition is that two vectors with coordinates and are added vectorially to produce a resultant vector with coordinates

42.
Refractive index
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In optics, the refractive index or index of refraction n of a material is a dimensionless number that describes how light propagates through that medium. It is defined as n = c v, where c is the speed of light in vacuum, for example, the refractive index of water is 1.333, meaning that light travels 1.333 times faster in a vacuum than it does in water. The refractive index determines how light is bent, or refracted. The refractive indices also determine the amount of light that is reflected when reaching the interface, as well as the angle for total internal reflection. This implies that vacuum has a index of 1. The refractive index varies with the wavelength of light and this is called dispersion and causes the splitting of white light into its constituent colors in prisms and rainbows, and chromatic aberration in lenses. Light propagation in absorbing materials can be described using a refractive index. The imaginary part then handles the attenuation, while the real part accounts for refraction, the concept of refractive index is widely used within the full electromagnetic spectrum, from X-rays to radio waves. It can also be used with wave phenomena such as sound, in this case the speed of sound is used instead of that of light and a reference medium other than vacuum must be chosen. Thomas Young was presumably the person who first used, and invented, at the same time he changed this value of refractive power into a single number, instead of the traditional ratio of two numbers. The ratio had the disadvantage of different appearances, newton, who called it the proportion of the sines of incidence and refraction, wrote it as a ratio of two numbers, like 529 to 396. Hauksbee, who called it the ratio of refraction, wrote it as a ratio with a fixed numerator, hutton wrote it as a ratio with a fixed denominator, like 1.3358 to 1. Young did not use a symbol for the index of refraction, in the next years, others started using different symbols, n, m, and µ. For visible light most transparent media have refractive indices between 1 and 2, a few examples are given in the adjacent table. These values are measured at the yellow doublet D-line of sodium, with a wavelength of 589 nanometers, gases at atmospheric pressure have refractive indices close to 1 because of their low density. Almost all solids and liquids have refractive indices above 1.3, aerogel is a very low density solid that can be produced with refractive index in the range from 1.002 to 1.265. Moissanite lies at the end of the range with a refractive index as high as 2.65. Most plastics have refractive indices in the range from 1.3 to 1.7, for infrared light refractive indices can be considerably higher

A laser is a device that emits light through a process of optical amplification based on the stimulated emission of …

A laser beam used for welding.

Laser beams in fog, reflected on a car windshield

A helium–neon laser demonstration at the Kastler-Brossel Laboratory at Univ. Paris 6. The pink-orange glow running through the center of the tube is from the electric discharge which produces incoherent light, just as in a neon tube. This glowing plasma is excited and then acts as the gain medium through which the internal beam passes, as it is reflected between the two mirrors. Laser output through the front mirror can be seen to produce a tiny (about 1 mm in diameter) intense spot on the screen, to the right. Although it is a deep and pure red color, spots of laser light are so intense that cameras are typically overexposed and distort their color.

Many of the differences between American and British English date back to a time when spelling standards had not yet …

Extract from the Orthography section of the first edition (1828) of Webster's "ADEL", which popularized the "American standard" spellings of -er (6); -or (7); the dropped -e (8); -or (10); -se (11); and the doubling of consonants with a suffix (15).

An 1814 American medical text showing British English spellings that were still in use ("tumours", "colour", "centres", etc.).

Fig. 1: Probability densities corresponding to the wave functions of an electron in a hydrogen atom possessing definite energy levels (increasing from the top of the image to the bottom: n = 1, 2, 3, ...) and angular momenta (increasing across from left to right: s, p, d, ...). Brighter areas correspond to higher probability density in a position measurement. Such wave functions are directly comparable to Chladni's figures of acoustic modes of vibration in classical physics, and are modes of oscillation as well, possessing a sharp energy and, thus, a definite frequency. The angular momentum and energy are quantized, and take only discrete values like those shown (as is the case for resonant frequencies in acoustics)

In this military radar, microwave radiation is transmitted between the source and the reflector by a waveguide. The figure suggests that microwaves leave the box in a circularly symmetric mode (allowing the antenna to rotate), then they are converted to a linear mode, and pass through a flexible stage. Their polarisation is then rotated in a twisted stage and finally they irradiate the parabolic antenna.

In quantum mechanics and particle physics, spin is an intrinsic form of angular momentum carried by elementary …

Schematic diagram depicting the spin of the neutron as the black arrow and magnetic field lines associated with the neutron magnetic moment. The neutron has a negative magnetic moment. While the spin of the neutron is upward in this diagram, the magnetic field lines at the center of the dipole are downward.

A magnetic field is a force field that is created by moving electric charges (electric currents) and magnetic dipoles, …

One of the first drawings of a magnetic field, by René Descartes, 1644, showing the Earth attracting lodestones. It illustrated his theory that magnetism was caused by the circulation of tiny helical particles, "threaded parts", through threaded pores in magnets.

The direction of magnetic field lines represented by the alignment of iron filings sprinkled on paper placed above a bar magnet.

A photon is a type of elementary particle, the quantum of the electromagnetic field including electromagnetic radiation …

The Wave–particle duality of light best explains the particle quanta and wave properties present in light, composed of photons representing the energy imparted by an electromagnetic wave.

In this illustration, one photon (purple) carries a million times the energy of another (yellow). Credit: NASA/Sonoma State University/Aurore Simonnet

Stimulated emission (in which photons "clone" themselves) was predicted by Einstein in his kinetic analysis, and led to the development of the laser. Einstein's derivation inspired further developments in the quantum treatment of light, which led to the statistical interpretation of quantum mechanics.

A polarizer or polariser is an optical filter that lets light waves of a specific polarization pass and blocks light …

A polarizing filter cuts down the reflections (top) and made it possible to see the photographer through the glass at roughly Brewster's angle although reflections off the back window of the car are not cut because they are less-strongly polarized, according to the Fresnel equations.

A stack of plates at Brewster's angle to a beam reflects off a fraction of the s-polarized light at each surface, leaving a p-polarized beam. Full polarization at Brewster's angle requires many more plates than shown. The arrows indicate the direction of the electrical field, not the magnetic field, which is perpendicular to the electric field

A wire-grid polarizer converts an unpolarized beam into one with a single linear polarization. Coloured arrows depict the electric field vector. The diagonally polarized waves also contribute to the transmitted polarization. Their vertical components are transmitted (shown), while the horizontal components are absorbed and reflected (not shown).

The electromagnetic waves that compose electromagnetic radiation can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. This diagram shows a plane linearly polarized EMR wave propagating from left to right (X axis). The electric field is in a vertical plane (Z axis) and the magnetic field in a horizontal plane (Y axis). The electric and magnetic fields in EMR waves are always in phase and at 90 degrees to each other.

Shows the relative wavelengths of the electromagnetic waves of three different colours of light (blue, green, and red) with a distance scale in micrometers along the x-axis.

In electromagnetic radiation (such as microwaves from an antenna, shown here) the term applies only to the parts of the electromagnetic field that radiate into infinite space and decrease in intensity by an inverse-square law of power, so that the total radiation energy that crosses through an imaginary spherical surface is the same, no matter how far away from the antenna the spherical surface is drawn. Electromagnetic radiation thus includes the far field part of the electromagnetic field around a transmitter. A part of the "near-field" close to the transmitter, forms part of the changing electromagnetic field, but does not count as electromagnetic radiation.